Keywords: Dedicated Optimization Solvers for Model Predictive Control, Optimization and Model Predictive Control, Real-Time Implementation of Model Predictive Control
Abstract: Concepts, algorithms and modeling platforms are described for the realization of nonlinear model predictive control (NMPC) using nonlinear programming (NLP). These allow the incorporation of predictive dynamic models that lead to high performance control, estimation and optimal operation. This talk reviews NLP formulations that guarantee properties for Lyapunov stability and extend to horizon lengths, terminal regions and costs. Moreover, fast algorithms for NMPC are briefly described and extended to deal with sensitivity-based solutions, as well as parallel decomposition strategies for large dynamic systems. Finally, Pyomo, a python-based modeling platform is tailored to deal with dynamic optimization strategies for state estimation, control and simulation, in order to incorporate all of these topics for on-line applications.

Keywords: Robust Model Predictive Control, Process Control
Abstract: In this work, we propose a framework for economic model predictive control (EMPC) with zone tracking. A zone tracking stage cost is incorporated into the existing EMPC framework to essentially form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the optimal steady state and characterize exact penalty for the zone tracking cost which prioritizes zone tracking objective over economic objective. A comprehensive study on the tradeoff between zone tracking and economic performance is carried out on a simple scalar linear system. Simulation results reveal intrinsic difficulties in parameter tuning due to the inconsistency between the zone tracking and economic objectives. A procedure to modify the target zone based on the economic performance and reachability of the optimal steady state is proposed. The modified target zone effectively decouples the dynamic zone tracking and economic objectives and simplifies parameter tuning.

Keywords: Robust Model Predictive Control, Real-Time Implementation of Model Predictive Control, Explicit Model Predictive Control
Abstract: In this paper, we propose a novel predictive control method suitable for low computing cost devices. The method consists of a finite step prediction filter and a simple compensator. The finite step prediction filter estimates future tracking error at Tp ahead from current at each step. The compensator is simple but the gain is calculated via a logical formula which represents future convergence of tracking error in time axis. A visualized method to guarantee robustness for model uncertainty is also proposed.

Keywords: Dedicated Optimization Solvers for Model Predictive Control, Real-Time Implementation of Model Predictive Control
Abstract: Pseudospectral and collocation methods form a popular direct approach to solving continuous-time optimal control problems. Lifted Newton-type algorithms have been proposed as a computationally efficient way to implement online pseudospectral methods for nonlinear model predictive control (NMPC). The present paper extends this work based on a rank-one Jacobian update formula for the nonlinear system dynamics. In addition, we describe an algorithm implementation where this rank-one Jacobian update can be used directly to compute a low-rank update to the condensed Hessian, resulting in an overall quadratic computational complexity for each iteration. A preliminary C code implementation is shown to allow considerable numerical speedups for the optimal control case study of the nonlinear chain of masses.

Keywords: Dedicated Optimization Solvers for Model Predictive Control, Real-Time Implementation of Model Predictive Control
Abstract: Model predictive control (MPC) often requires solving an optimal control structured quadratic program (QP), possibly based on an online linearization at each sampling instant. Block-tridiagonal preconditioners have been proposed, combined with the minimal residual (MINRES) method, to result in a simple but efficient implementation of a sparse active-set strategy for fast MPC. This paper presents an improved variant of this PRESAS algorithm, by using a projected preconditioned conjugate gradient (PPCG) method. Based on a standalone C code implementation and using an ARM Cortex-A7 processor, we illustrate the performance of the proposed solver against the current state of the art for embedded predictive control.

Keywords: Distributed Model Predictive Control, Real-Time Implementation of Model Predictive Control, Process Control
Abstract: A coordination scheme for nonlinear MPCs is presented using a dynamic real-time optimization (DRTO) formulation with a nonlinear dynamic plant model. By considering the control action of constrained nonlinear MPCs, the nonlinear DRTO formulation generates the predicted closed-loop response of the plant and computes optimal set-point trajectories based on an economic objective. The set-point trajectories are assigned to lower-level nonlinear MPCs for tracking. Due to the inclusion of nonlinear MPC regulation, the DRTO formulation results in a multi-level optimization problem. The solution strategy applied is to transform the nonlinear MPC optimization subproblems into sets of algebraic equations using the Karush-Kuhn-Tucker (KKT) optimality conditions, and to embed these equations in the DRTO formulation to yield a single-level optimization problem. The performance of proposed formulation is evaluated through application to a case study, with comparisons made against its counterpart that utilizes linear DRTO and MPC formulations.

Keywords: Distributed Model Predictive Control, Process Control
Abstract: An approach to low complexity distributed MPC of nonlinear interconnected systems with coupled dynamics subject to both state and input constraints is proposed. It is based on the idea of introducing a contractive constraint in the centralized NMPC problem formulation, which would guarantee the closed-loop system stability when using a small prediction horizon. Particularly, the one step ahead NMPC problem is considered. Further, a quasi-NMPC method is developed, which is based on a sequential linearization of the nonlinear system dynamics and finding distributedly a suboptimal solution of the resulting convex Quadratically Constrained Quadratic Programming problem. The suggested approach would be appropriate for distributed convex NMPC of some cyber-physical systems, since it will reduce the complexity of the on-line NMPC computations, simplify the software implementation, and reduce the requirements for available memory. The proposed method is illustrated with simulations on the model of a quadruple-tank system.

Keywords: Process Control, Explicit Model Predictive Control, Stability and Recursive Feasibility
Abstract: This work focuses on the design of a new class of economic model predictive control (EMPC) systems for nonlinear systems that address simultaneously the tasks of economic optimality, safety and closed-loop stability. This is accomplished by incorporating in the EMPC an economics-based cost function and Control Lyapunov-Barrier Function (CLBF)-based constraints that ensure that the closed-loop state does not enter unsafe sets and remains within a well-characterized set in the system state-space. The new class of CLBF-EMPC systems is demonstrated using a nonlinear chemical process example.

Keywords: Stability and Recursive Feasibility
Abstract: Model Predictive Control (MPC) is a moving horizon scheme for stabilizing a plant to an operating point. It's generalization, Model Predictive Regulation (MPR), is a moving horizon scheme for tracking a reference signal or rejecting a known disturbance. Adaptive Horizon Model Predictive Regulation (AHMPR) is a scheme for varying as needed the length of the horizon of Model Predictive Regulation. Its goal is to achieve tracking or disturbance rejection with horizons as small as possible. This allows AHMPR to be used on faster and/or more complicated dynamic processes

Keywords: Stability and Recursive Feasibility
Abstract: Model predictive control (MPC) is the standard approach to infinite-horizon optimal control which usually optimizes a finite initial fragment of the cost function so as to make the problem computationally tractable. Globally optimal controllers are usually found by Dynamic Programming (DP). The computations involved in DP are notoriously hard to perform, especially in online control. Therefore, different approximation schemes of DP, the so-called ``critics'', were suggested for infinite-horizon cost functions. This work proposes to incorporate such a critic into dual-mode MPC as a particular means of addressing infinite-horizon optimal control. The proposed critic is based on Q-learning and is used for online approximation of the infinite-horizon cost. Stability of the new approach is analyzed and certain sufficient stabilizing constraints on the critic are derived. A case study demonstrates the applicability.

Keywords: Robust Model Predictive Control, Stability and Recursive Feasibility, Real-Time Implementation of Model Predictive Control
Abstract: In case when a nonlinear system is represented by quasi-LPV model with bounded disturbance, we adopt the parameter-dependent dynamic output feedback MPC (PDDOFMPC) with guaranteed quadratic boundedness and physical constraints. We pre-specify one sequence of nested ellipsoids for estimated state, and another for estimation error, then calculate PDDOFMPC parameters for each combination of estimated state ellipsoid and estimation error ellipsoid. A look-up table is constructed off-line to store these controller parameters each related to a unique combination. On-line, the estimated state is iterated and the estimation error set is refreshed. By checking the smallest off-line estimated state ellipsoid to contain the real-time estimated state, and the smallest off-line estimation error ellipsoid to include the real-time estimation error set, a unique set of control parameters is taken from the look-up table at each sampling instant. An example is given to illustrate the effectiveness of the approach.

Keywords: Robust Model Predictive Control, Process Control
Abstract: In this paper, we present an implicit dual robust nonlinear model predictive control in the framework of (bounded-error) guaranteed parameter estimation and multi-stage NMPC, which uses a scenario-tree to represent propagation of parametric model uncertainty through a dynamic system. The proposed implicit dual control scheme excites the system if the excitation signals improve the overall performance of the controller. A box (over-)approximation of the solution set of guaranteed parameter estimation which encloses the true parameter values is obtained by solving an optimization problem. The proposed approach uses approximations of the future solution sets and updates the scenario tree of the multi-stage NMPC along the prediction horizon accordingly. This gives rise to a bi-level optimization problem, which is solved as a single-level problem by implicitly solving the lower-level problem using its KKT conditions. The advantages of the proposed approach over the standard multi-stage NMPC are demonstrated for a linear and nonlinear (semi-batch reactor) simulation case studies.

Keywords: Sub-Optimal Model Predictive Control, Motion Control
Abstract: This paper proposes a novel sub-optimal nonlinear moving horizon estimation (NMHE) algorithm tailored to underactuated mechanical systems. We utilize the special variational structure of the mechanical systems and achieve numerical integration in NMHE via variational integrators. The resulting NMHE algorithm is based on the optimal control method Discrete Mechanics and Optimal Control (DMOC). It has significantly less number of optimization variables and is numerically more efficient than the standard NMHE algorithm based on multiple-shooting (MS). We use detailed numerical analysis with a double pendulum on a cart system to demonstrate that the novel NMHE algorithm outperforms the famous Extended Kalman Filter and is more efficient than the standard NMHE approach based on MS and the partial condensing technique in the chosen application. We also show closed-loop simulation results with the combined DMOC-based NMHE-NMPC framework for the swing-up and stabilization of the double pendulum system.

Keywords: Distributed Model Predictive Control
Abstract: The interconnection of dynamically decoupled subsystems, each exhibiting a certain dissipativity property considered in the context of economic MPC, is investigated. Interconnection of the subsystems is by means of their cost functions being separable in a purely local economic and a coupling cost term. For certain classes of quadratic interconnection costs we provide conditions on the interconnection structure under which the overall system exhibits the same dissipativity property. Moreover, we apply a non-iterative distributed MPC scheme to the interconnected system which yields asymptotic stability of the overall optimal steady state by exploiting the structural properties of the system interconnection.

Keywords: Economic Predictive Control, Optimization and Model Predictive Control, Process Control
Abstract: Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of {plant-model} mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example.

Keywords: Stability and Recursive Feasibility, Robotics
Abstract: This paper considers an NMPC (Nonlinear Model Predictive Control) scheme which includes a CTC (Computed-Torque Control) law for ensuring recursive feasibility and asymptotic stability guarantees. Specifically, the CTC law leads to stable linear closed-loop dynamics. By choosing appropriate control gains, a positive invariant ellipsoidal set in which the input constraints are satisfied is determined. Using this set as terminal region in the NMPC problem, together with additional assumptions provides asymptotic stability guarantees. Simulation results and comparisons with quasi-infinite horizon NMPC over a particular system, an inverted pendulum, prove the efficiency of the proposed NMPC scheme.

Keywords: Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: We are concerned with Model Predictive Control (MPC) of constrained linear systems governed by regular differential-algebraic equations. The contribution is twofold: First, we provide a characterization of the set of admissible control functions to clarify what the actual input is. This is essential for the design of numerical algorithms. Secondly, we present a blueprint for the construction of suitable terminal costs and terminal constraints such that asymptotic stability of the origin w.r.t. the MPC closed-loop is guaranteed provided initial feasibility. To this end, we exploit recent results on the unconstrained linear quadratic regulator problem using recently introduced concepts of input index and an augmented system.

Keywords: Stability and Recursive Feasibility, Real-Time Implementation of Model Predictive Control, Optimization and Model Predictive Control
Abstract: In this work, we address through model predictive control (MPC) a constrained nonlinear plant described by a continuous-time dynamical model, which naturally leads to a sampled-data control system. The numerical solution of the optimal control problems involved in MPC must use, eventually, some form of discretization. Nevertheless, there are several advantages in maintaining a continuous-time model until later stages. One advantage is that we can devise numerical procedures which, by exploiting additional freedom in selecting the discretization points, are more efficient when continuous-time models are used. Here, we discuss an extension to MPC of an Adaptive Mesh Refinement (AMR) algorithm, which has shown to be efficient in solving nonlinear optimal control problems. We derive a sufficient condition that guarantees that an MPC scheme using an adaptive time-mesh refinement algorithm preserves stability.

Keywords: Economic Predictive Control, Process Control
Abstract: Increasing pushes toward next-generation/smart manufacturing motivate the development of economic model predictive control (EMPC) designs which can be practically deployed. For EMPC, the constraints and objective function, as well as the accuracy of the state predictions, would benefit from process models which describe the process physics. However, obtaining first-principles models of chemical process systems can be time-consuming or challenging, motivating the investigation of the development of physically-based process models from process operating data. In this work, we take initial steps in this direction by suggesting that because experiments that are used to characterize first-principles models often target very specific types of data, an EMPC may be utilized to gather non-routine operating data with the goal of seeking data that may aid in better understanding the process physics and thereby developing physics-based process models on-line. These models can then be used to update the model, objective function, and constraints of the controller. Closed-loop stability and recursive feasibility considerations are discussed for the proposed EMPC design, and a chemical process example illustrates the application of the proposed controller.

Keywords: Stability and Recursive Feasibility, Process Control
Abstract: In this work, we propose a new approach based on a discrete time linear quadratic regulator (LQR) for characterization of terminal region in discrete time quasi-infinite horizon NMPC. Further, we propose a practical method of bounding only the higher order nonlinear effects of the system under LQR control. This leads to a method of calculating the terminal region for a large dimensional system. Efficacy of the proposed approaches for terminal region computation is demonstrated using a benchmark CSTR system and a large scale system consisting of two distillation columns in series. Simulation results demonstrate that the proposed approaches provide sufficient degrees of freedom to shape the terminal region.

Keywords: Learning and Predictive Control, Process Control
Abstract: Control of a system exhibiting input multiplicity at an optimum (singular) operating point poses a challenging control problem due to loss of invertibility and change in the sign of the steady state gain in the neighborhood of the optimum. In this work, for controlling systems exhibiting input multiplicities, we develop a novel adaptive dual NMPC (ADNMPC) formulation based on a Wiener model which is parameterized using orthonormal basis filters (OBF). The static nonlinear output map in the Wiener model is constructed using multi-dimensional quadratic polynomials. The OBF poles are chosen through an off-line identification exercise and the parameters of the static nonlinear map are updated on-line using recursive least squares algorithm. Similar to Kumar et al. (2017), by introducing concept of excitation horizon, the objective function in the NMPC formulation is modified to include terms that are sensitive to the parameter covariance. The proposed formulation provides sufficient degrees of freedom to shape the probing signals. Efficacy of the proposed approach is demonstrated by simulating problem of controlling a continuously operated fermenter system at its optimum operating point. Analysis of the simulation results shows that the proposed ADNMPC scheme judiciously injects perturbations into the process as and when required. The probing perturbations subside when the parameter estimates stabilize. In particular, it is observed that the intensity of the perturbation increase as the excitation horizon increases. The proposed on-line model adaptation also ensures better control performance with reference to a non-adaptive NMPC controller.

Keywords: Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: We consider model predictive control (MPC) without stabilizing terminal constraints and costs for systems governed by linear Differential-Algebraic Equations. To this end, an augmented system is introduced to derive an equivalent formulation of the underlying Optimal Control Problem to be solved in each MPC iteration, which is only constrained by an Ordinary Differential Equation. This facilitates the analysis and the computation of a prediction horizon such that asymptotic stability of the origin w.r.t. the MPC closed-loop is guaranteed.

Keywords: Economic Predictive Control, Process Control, Tracking and Path Following Predictive Control
Abstract: This paper proposes an Economic Predictive Control strategy for TISO processes based on the Generalized Predictive Control (GPC). In the absence of input or output constraints the proposed controller has the form of classical state observer, which is useful for dealing with practical issues. Simulation for the constrained case is performed in order to show effectiveness of the proposal.

Keywords: Robust Model Predictive Control
Abstract: We present a real-time implementable robust Nonlinear Model Predictive Control (NMPC) framework that simultaneously addresses model uncertainty and unmeasured disturbances based on a multistage scenario tree to describe evolution of uncertainties. The multistage scenario tree computes a control action that hedges against all possible uncertainty realizations and optimizes expected performance. However, the scenario tree structure inevitably increases the optimization problem size, as robust horizons become longer. This presents a challenge to solve the large-scale problem in real-time. We propose the parallelizable advanced-step multistage NMPC (as-msNMPC) that precomputes a set of solutions in background so that the online computation effort is negligible. We apply as-msNMPC framework to a CSTR example to show the controller's robustness and improved online performance over competing robust NMPC methods.

Keywords: Hybrid Model Predictive Control, Stability and Recursive Feasibility, Robotics
Abstract: This paper presents a model predictive control (MPC) algorithm that asymptotically stabilizes a compact set of interest for a given hybrid dynamical system. The considered class of systems are described by a general model, which identifies the dynamics by the combination of constrained differential and difference equations. The model allows for trajectories that exhibit multiple jumps at the same time instant, or portray Zeno behavior. At every optimization time, the proposed algorithm minimizes a cost functional weighting the state and the input during both the continuous and discrete phases, and at the terminal time via a terminal cost, without discretizing the continuous dynamics. To account for the structure of time domains defining solution pairs, the minimization is performed in a manner akin to free end-time optimal control. When the terminal cost is a control Lyapunov function on the terminal constraint set, recursive feasibility and asymptotic stability of the proposed algorithm can be guaranteed. A sample-and-hold control system and a bouncing ball model are two examples reported to demonstrate the applicability and effectiveness of the proposed approach.

Keywords: Output Feedback Predictive Control, Robust Model Predictive Control, Stability and Recursive Feasibility
Abstract: Optimal design and tuning of model predictive controllers is important as it significantly influences the achievable performance. We consider the problem of tuning a tube based robust predictive output feedback controller, which utilizes a linear feedback - the tube controller - to take the uncertainties into account. The design and the tuning of this linear feedback has a big influence on the tube and thus the resulting overall performance. We propose a tuning exploiting the Youla parametrization leading to a convex optimization problem. Conditions are provided to guarantee robust constraint satisfaction and robust set- point tracking. The results are illustrated by examples.

Keywords: Stability and Recursive Feasibility
Abstract: The terminal cost and terminal set method for guaranteeing stability of nonlinear model predictive control (MPC) closed-loop systems is theoretically appealing but often impractical. This is due to the difficulty of computing invariant sets and control Lyapunov functions for general nonlinear systems. In this paper we propose a novel method for computing time-varying terminal costs and sets by means of first order or second order Taylor approximations of the nonlinear system dynamics. The method first solves a set of linear matrix inequalities to compute the terminal ingredients for the approximated dynamics. Then, a small scale global nonlinear optimization problem is solved to check the validity of the terminal ingredients for the nonlinear dynamics. The proposed method also allows for time-varying linear or nonlinear terminal control laws. The developed method can result in significant enlargements of the domain of attraction of the nonlinear MPC closed-loop system, as demonstrated by a benchmark academic example.

Keywords: Optimization and Model Predictive Control, Real-Time Implementation of Model Predictive Control
Abstract: In this paper, we consider a problem of designing discrete-time systems which are optimal in frequency-weighted least squares sense subject to a maximal output amplitude constraint. It can be shown for such problems, in general, that the optimality conditions do not provide an explicit way of generating the optimal output as a real-time implementable transformation of the input, due to the instability of the resulting dynamical equations and sequential nature in which criterion function is revealed over time. In this paper, we show that, under some mild assumptions, the optimal system has exponentially fading memory. We then propose a causal and stable finite-dimensional nonlinear system which, under an L1 dominance assumption about the equation coefficients, returns high-quality approximations to the optimal solution. The fading memory of the optimal system justifies the receding horizon assumption and suggests that such an approach can serve as a cheaper alternative to standard MPC-based algorithms. The result is illustrated on a problem of minimizing peak-to-average-power ratio of a communication signal, stemming from power-efficient transceiver design in modern digital communication systems.

Keywords: Tracking and Path Following Predictive Control, Stability and Recursive Feasibility, Robotics
Abstract: In this paper, we propose an extension to the existing Model Predictive Control scheme for tracking. This extension is able to provide a solution for the case where the set of steady-state admissible outputs is non-convex. This is achieved by means of a transformation that maps the output set into a convex set. In the proposed scheme, the cost function and constraints of the usual tracking MPC are modied, so that the controller can drive the system to any point in the admissible steady-state domain without violating any constraints. The paper discusses the feasibility and stability of the proposed approach and a nal simulation demonstrates the effectiveness of the approach.

Keywords: Economic Predictive Control, Optimization and Model Predictive Control, Robust Model Predictive Control
Abstract: Economic model predictive control (EMPC) provides a seamless integration between real-time optimization (RTO) and dynamic optimization layers in the process control hierarchy, removing time-scale separation in the conventional two-layer MPC implementation. In this work, we present an algorithm for one-layer EMPC, where the RTO and dynamic optimization are performed simultaneously. Steady-state point is included as an optimization variable in the dynamic optimization, denoted as artificial steady-state point. The advantage of applying the one-layer EMPC is that it can capture parameter changes during the course of EMPC running, such as price information. The only design parameter for the one-layer EMPC is stage cost without the presence of terminal conditions (terminal penalty and terminal constraint), assuming strict dissipativity property and reachability condition. In order to handle parametric uncertainty, we employ a multistage model predictive control approach in an advanced-step NMPC (asNMPC) framework that consists of online and offline steps. This allows a parallel run of nonlinear programming (NLP) solver for each scenario in the offline step, and fast sensitivity update using a path-following method in the online step. We assess the proposed algorithm in a simple case example, describing an isothermal CSTR process. It is shown that the algorithm is able to steer the resulting closed-loop system to steady-state points in the presence of parameter changes. Moreover, the multistage EMPC gives a similar result to that of nominal EMPC despite of parameter uncertainty.

Keywords: Explicit Model Predictive Control, Optimization and Model Predictive Control
Abstract: On-line tuning of explicit MPC controllers is one of the most important aspects when considering a practical implementation of such controllers. Although explicit MPC allows for a fast, simple, and cheap implementation of optimal control to constrained systems with a fast dynamics, such controllers can only be synthesized for a fixed choice of the tuning parameters and do not allow the control engineer to adjust them on-the-fly. In this contribution we propose an interpolation-based approach to on-line tuning of explicit MPC. The scheme operates with two or multiple explicit controllers obtained for a different selection of the tuning parameters. Then, should these parameters change on-line, an approximate control action is computed via a linear or a piecewise linear interpolation.

Keywords: Dedicated Optimization Solvers for Model Predictive Control
Abstract: Model Predictive Control (MPC) has become one of the most popular techniques adopted in industry to control multivariable systems in an optimized way under constraints on input and output variables. MPC hinges upon the availability of good dynamical models for prediction and good numerical solvers for real-time computations. For MPC to be applicable in industrial production one would like to reduce the time/difficulty involved in developing prediction models and also to have solvers that require limited resources (CPU time, memory), are numerically very robust, and are certifiable for worst-case execution time. In my talk I will present recent developments in data-driven design of MPC controllers and in embedded quadratic optimization, giving a concrete example of designs of multivariable MPC systems that are scheduled for mass production in the automotive industry in 2018.

Keywords: Economic Predictive Control
Abstract: Recently, it has been shown in a sampled-data continuous-time setting that under certain regularity assumptions a simple linear end penalty enforces exponential stability of Economic (nonlinear) Model Predictive Control (EMPC) without terminal constraints. This paper investigates the same framework in the discrete-time case, i.e. we establish sufficient conditions for asymptotic stability of the optimal steady state under an EMPC scheme without terminal constraints. The key ingredient is a linear end penalty that can be understood as a gradient correction of the stage cost by means of the adjoint/dual variable of the underlying steady-state optimization problem. Although almost all stability proofs for EMPC focus on primal variables, our developments elucidate the importance of the adjoints for achieving asymptotic stability without terminal constraints. Moreover, we propose an adaptive gradient correction strategy which alleviates the need for solving explicitly the steady-state optimization. Finally, we draw upon two simulation examples to illustrate our results.

Keywords: Robust Model Predictive Control, Stochastic Model Predictive Control, Stability and Recursive Feasibility
Abstract: Two competing versions for robust and stochastic model predictive control of constrained linear systems are compared and contrasted. Implications for robust and stochastic model predictive control are discussed.

Keywords: Real-Time Implementation of Model Predictive Control, Optimization and Model Predictive Control, Stability and Recursive Feasibility
Abstract: This paper discusses systems theoretic and computational aspects of a feasible, but suboptimal, nonlinear model predictive control scheme based on fixed sensitivities of the functions representing the constraints and cost of the underlying nonlinear programs. In particular, it will be shown how, by freezing the sensitivities computed at the desired steady state of the system, an efficient, structure-exploiting scheme is obtained that can considerably speed up the computations required for both construction and solution of the quadratic subproblems. Moreover, the local stability properties of the converged solution are analysed using results on pseudoexpansions of generalized equations present in the literature. The effectiveness of the proposed scheme is demonstrated on a non-trivial benchmark where large speedups can be achieved.