In this dissertation, we study the interaction between the control performance and the quality of the state estimation in a constrained Model Predictive Control (MPC) framework for systems with stochastic disturbances. This consists of three parts: (i) the development of a constrained MPC formulation that adapts to the quality of the state estimation via constraints; (ii) the application of such a control law in a multi-vehicle formation coordinated control problem in which each vehicle operates subject to a no-collision constraint posed by others' imperfect prediction computed from finite bit-rate, communicated data; (iii) the design of the predictors and the communication resource assignment problem that satisfy the performance requirement from Part (ii). Model Predictive Control (MPC) is of interest because it is one of the few control design methods which preserves standard design variables and yet handles constraints. MPC is normally posed as a full-state feedback control and is implemented in a certainty-equivalence fashion with best estimates of the states being used in place of the exact state. However, if the state constraints were handled in the same certainty-equivalence fashion, the resulting control law could drive the real state to violate the constraints frequently. Part (i) focuses on exploring the inclusion of state estimates into the constraints. It does this by applying constrained MPC to a system with stochastic disturbances. The stochastic nature of the problem requires re-posing the constraints in a probabilistic form. Using a gaussian assumption, the original problem is approximated by a standard deterministic constrained MPC problem or the conditional mean process of the state (the prediction). The state estimates' conditional covariances appear in tightening the constraints as measuring the necessary standoff from the bound on the real state. `Closed-loop covariance' is introduced to reduce the infeasibility and the conservativeness caused by using long-horizon, open-loop prediction covariances. The resulting control law is applied to a telecommunications network traffic control problem as an example. The idea of posing and transforming a probabilistic MPC problem works well, but not limited to, linear systems. In Part (ii), we consider applying constrained MPC as a local control law in a coordinated control problem of a group of distributed autonomous systems. Interactions between the systems are captured via constraints. First, we inspect the application of constrained MPC to a completely deterministic case. Formation stability theorems are derived for the subsystems and conditions on the local constraint set are derived in order to guarantee local stability or convergence to a target state. If these conditions are met for all subsystems, then this stability is inherited by the overall system. For the case when each subsystem suffers from disturbances in the dynamics, own self-measurement noises, and quantization errors on neighbors' information due to the finite-bit-rate channels, the constrained MPC strategy developed in Part (i) is appropriate to apply. Disturbance attenuation, or ``string stability", is studied in this framework and it is shown that inactivity of the MPC constraints implies stability. This then provides a connection between control objective, communications resource assignment and performance. A one-dimensional vehicle example is computed to crystallize ideas. The application of this part is not restricted to linear systems. In Part (iii), we discuss the local predictor design and bandwidth assignment problem in a coordinated vehicle formation context. The MPC controller used in Part (ii) relates the formation control performance and the information quality in the way that large standoff implies conservative performance. If the communication channels used to exchange local information are noiseless, but have only finite bit-rate, the bits assigned to each variable in the information package will change the prediction error covariance, and hence the control performance, via the quantization errors which can be regarded as measurement noises. In this part, we aim at deriving the minimal communication resource and the corresponding bit-rate assignment strategy the corresponding stable state predictors that is used to formulate the MPC constraints. We first develop an LMI (Linear Matrix Inequality) formulation for cross-estimator design in a simple two-vehicle scenario with non-standard information: one vehicle does not have access to the other's exact control value applied at each sampling time, but to its known, pre-computed, coupling linear feedback control law. Then a similar LMI problem is formulated for the bandwidth assignment problem that minimizes the total number of bits by adjusting the prediction gain matrices and the number of bits assigned to each variable. This LMI formulation takes care of the constraint on steady state prediction error covariance imposed by the formation performance requirement, the constraint on the limited total bandwidth, and the constraint on the predictors being stable. Some linear approximation is used to include the bandwidth assignment variables in the LMI formulation. The solution of the resulting LMIs guarantees the feasibility of the bandwidth assignment scheme and stable predictors, but not optimality. An example of a three-vehicle formation is also provided. The LMI formulation here is restricted to linear systems.

Recent developments in constrained control and estimation have created a need for this comprehensive introduction to the underlying fundamental principles. These advances have significantly broadened the realm of application of constrained control. - Using the principal tools of prediction and optimisation, examples of how to deal with constraints are given, placing emphasis on model predictive control. - New results combine a number of methods in a unique way, enabling you to build on your background in estimation theory, linear control, stability theory and state-space methods. - Companion web site, continually updated by the authors. Easy to read and at the same time containing a high level of technical detail, this self-contained, new approach to methods for constrained control in design will give you a full understanding of the subject.

In this thesis, two subjects are considered: new techniques to improve stabilizing performance and feasibility in model predictive control and disturbance rejection control in coordinated systems. Model predictive control is powerful when a system has constraints. However, by nature, feasibility and stabilizing property of model predictive control can be lost without proper treatments. A new idea is studied for the case that a system is not well stabilized by classical model predictive control since the origin is not reachable from initial states in a limited horizon. We handle this matter by using a time-varying contractive terminal state equality constraint in model predictive control. The core condition to execute our idea is a structural property of the system such as contractibility or a known control lyapunov function. In addition, algorithmic approaches to guarantee feasible model predictive control are developed with several state constraint structures. Assuming that the model predictive control problem at current time is feasible, we want to know the set of terminal states or new references such that the problem at the next time instant is still feasible. Solutions are given for the linear system case using reachability analysis. The rest of the talk considers disturbance rejection control in coordinated systems. We employ a fixed vehicle formation problem as a working problem. The aim is to design a controller to maintain the formation and avoid collisions in the presence of disturbance, measurement, and communication noises. Each vehicle has its own local controller that uses the state and input information from neighbors via communication. We formulate local model predictive control and estimators for one vehicle to estimate the states of the neighboring vehicles. Since coordinated systems interact via the exchange of information through communication, as the network of coordinated systems increases in the number of subsystems, natural limits on the available bandwidth of communication need to be imposed. With the gaussian assumptions on the noises and disturbance, the estimators are designed by linear matrix inequality methods, which link control objective, estimation performance, and communication limits. Even when bounds on the uncertainties are known instead of the gaussian assumptions, controllers and estimators can be formulated. Case studies are provided to demonstrate the main ideas and discuss interesting design issues.

During the past decade model predictive control (MPC), also referred to as receding horizon control or moving horizon control, has become the preferred control strategy for quite a number of industrial processes. There have been many significant advances in this area over the past years, one of the most important ones being its extension to nonlinear systems. This book gives an up-to-date assessment of the current state of the art in the new field of nonlinear model predictive control (NMPC). The main topic areas that appear to be of central importance for NMPC are covered, namely receding horizon control theory, modeling for NMPC, computational aspects of on-line optimization and application issues. The book consists of selected papers presented at the International Symposium on Nonlinear Model Predictive Control – Assessment and Future Directions, which took place from June 3 to 5, 1998, in Ascona, Switzerland. The book is geared towards researchers and practitioners in the area of control engineering and control theory. It is also suited for postgraduate students as the book contains several overview articles that give a tutorial introduction into the various aspects of nonlinear model predictive control, including systems theory, computations, modeling and applications.

This monograph introduces the authors’ work on model predictive control system design using extended state space and extended non-minimal state space approaches. It systematically describes model predictive control design for chemical processes, including the basic control algorithms, the extension to predictive functional control, constrained control, closed-loop system analysis, model predictive control optimization-based PID control, genetic algorithm optimization-based model predictive control, and industrial applications. Providing important insights, useful methods and practical algorithms that can be used in chemical process control and optimization, it offers a valuable resource for researchers, scientists and engineers in the field of process system engineering and control engineering.

Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive control with respect to both theoretical and application aspects. Over these 30 years, model predictive control for linear systems has been widely applied, especially in the area of process control. However, today’s applications often require driving the process over a wide region and close to the boundaries of - erability, while satisfying constraints and achieving near-optimal performance. Consequently, the application of linear control methods does not always lead to satisfactory performance, and here nonlinear methods must be employed. This is one of the reasons why nonlinear model predictive control (NMPC) has - joyed signi?cant attention over the past years,with a number of recent advances on both the theoretical and application frontier. Additionally, the widespread availability and steadily increasing power of today’s computers, as well as the development of specially tailored numerical solution methods for NMPC, bring thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has led to a series of new, exciting developments, along with new challenges in the area of NMPC.