More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the on-line optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for nonlinear systems but for practical applications many questions remain, including the reliability and efficiency of the on-line computation scheme. To deal with model uncertainty "rigorously" an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, nonlinear state estimation, and batch system control. Many practical problems like control objective prior...

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Changing product specications and load changes require that operating points have to be changed frequently during the operation of many processes. The nonlinear model predictive control (NMPC) schemes available at present that guarantee stability of the closed loop are, however, only suited to stabilize the behavior around one priori known steady state. The possibility for setpoint changes is not considered in the setup for these NMPC schemes and if this is incorporated in an ad hoc manner, stability cannot be guaranteed for varying setpoints. In this paper a new approach based on the wellknown pseudolinearization in connection with the quasi-innite horizon NMPC scheme is presented, that allows the stabilization not only around one setpoint, but rather of a whole family of setpoints. The pseudolinearization is used to obtain a closed expression for the controller parameters as a function of the setpoints, such that for every setpoint stability of the closed loop is guaranteed. The method is applied in simulation to the control of a chemical reactor.

Varying product speci cations and load changes require that operating points have to be changed frequently during the operation of many processes. Hence controllers have to guarantee stability for all setpoints and allow smooth transfer between setpoints. We propose to combine pseudolinearization and quasi-in nite horizon nonlinear predictive control for the solution of this problem. The pseudolinearization is used to obtain a closed expression for the controller parameters as a function of the setpoints, such that for every setpoint stability of the closed loop is guaranteed.

Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. Extending the concept of solving the Hamilton--Jacobi--Bellman equation backwards (the so--called "converse HJB approach") to the constrained case provides a method to generate various classes of challenging nonlinear benchmark examples, where the true constrained optimal controller is known. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization. 1 Introduction Determination of the optimal feedback law for nonlinear optimal control problems require solutions of Hamilton-Jacobi--Bellman (HJB) partial differential equations. Difficulties in solving the HJB equation ...

We present a new approach to the stability analysis of finite receding horizon control applied to constrained linear systems. By relating the final predicted state to the current state through a bound on the terminal cost, it is shown that knowledge of upper and lower bounds for the finite horizon costs are sufficient to determine the stability of a receding horizon controller. This analysis is valid for receding horizon schemes with arbitrary positive-definite terminal weights, and does not rely on the use of stabilizing constraints. The result is a computable test for stability, and two simple examples are used to illustrate its application. Keywords: predictive control, constrained systems, linear systems, discrete time. 1 Introduction Receding horizon control (RHC), also known as model predictive control (MPC) [8], is an on-line technique in which a new control action is computed at each time step by solving a finite horizon optimization problem that extends from the current time ...

The issue of optimality in nonlinear controller design is confronted by using the converse HJB approach [1] to classify dynamics under which certain design schemes are optimal. In particular, the techniques of Jacobian linearization, pseudo-Jacobian linearization, and feedback linearization are analyzed. Finally, the conditions for optimality are applied to the 2-D nonlinear oscillator, where simple, nontrivial examples are produced in which the various design techniques are optimal. 1 Introduction Determination of the optimal feedback law for nonlinear optimal control problems requires the solution of the Hamilton-Jacobi--Bellman (HJB) partial differential equation. Difficulties in solving the HJB equation for high dimensional systems have precluded their use except in specific areas, and have motivated the study of alternative control techniques. Many of such alternative techniques attempt to "approximately" solve the HJB equation by using some simplified scheme (Jacobian linearizat...

We present and compare various extensions of Model Predictive Control (MPC) to the class of both full state and input/output feedback linearizable systems. The presented approaches are valid even for systems with unstable zero dynamics, with the goal being a reduction of the burdensome computational costs typically associated with nonlinear MPC. Finally, these various approaches are tested on examples. 1. Introduction Determination of the optimal feedback law for nonlinear optimal control problems requires the solution of the Hamilton-Jacobi--Bellman (HJB) partial differential equation. Difficulties in solving the HJB equation for high dimensional systems have precluded its use except in specific areas, and have motivated the study of alternative control techniques. One such technique is model predictive control (MPC), also known as moving or receding horizon control, which uses on--line optimization and a receding horizon implementation [1]. In addition, MPC naturally and explicitly...

Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC--based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then e...

A hybrid control strategy integrating neural networks into the predictive control scheme and a first principle model predictive control technique for controlling purposes of non-linear plants are presented and compared. The neural network approach involves a recurrent Elman network to capture the dynamics of the plant to be controlled being the learning stage implemented on-line using a modified backpropagation through time algorithm. The predictive control scheme is implemented by an iterative and repetitive optimisation process. Within the first principle model predictive control framework a local linearisation of the mathematical model of the non-linear plant followed by a discrete-time approximation is performed at each sampling time. Next, a real-time open-loop linear constrained optimisation problem is solved with a standard quadratic programming algorithm. Experimental results collected from an interconnected three-tanks system are presented and discussed for both control techni...