Edward S. Meadows

Discrete-time stability with perturbations: application to model predictive control

Exponential stability and asymptotic perturbed stability results are derived for nonlinear discrete-time systems. Some related results are available in the literature, but proofs for the discrete-time case are difficult to find. Our motivation for obtaining these results was to determine conditions under which discrete-time nonlinear model predictive control is stabilizing in the face of perturbations. This problem has particular relevance when output (rather than state) feedback is used. A nonlinear state estimator is then required to reconstruct the state, and it is necessary to identify the class of reconstruction errors for which the cascaded estimator/controller assembly is stabilizing.

Nonlinear Model Predictive Control: A Tutorial and Survey

Abstract This paper presents a tutorial survey of model predictive control for constrained linear plants and nonlinear plants. A streamlined implementation is presented for constrained linear systems. The formulation is shown to be nominally stabilizing in the presence of constraints provided inconsistent state constraints are relaxed. Cases with incomplete state measurement and nonzero set points are also discussed. A constant output disturbance model is shown to provide offset free integral control. The differences between optimal control and model predictive control are illustrated with a stochastic control example. Nominal stability is proved for a class of nonlinear plants. The major topics of current research in the field are summarized.

Receding horizon control and discontinuous state feedback stabilization

This paper addresses three aspects of receding horizon control in discrete-time: (1) feedback stabilization of general nonlinear systems with receding horizon control; (2) the generation of stabili...

Receding Horizon Control with an Infinite Horizon

Receding horizon control, also called model predictive control, is an optimal control-based method for finding constrained feedback controllers. Several of the standard formulations provide no stability guarantees even if an optimum exists. In this paper, we extend the concept of model predictive control to an infinite horizon to show that such a formulation guarantees the stability of the resulting feedback controller. We also introduce a framework for analysis of receding horizon controllers that will allow future study of other important properties of receding horizon controllers, such as robustness and continuity of feedback control laws.

Topics in Model Predictive Control

This paper discusses two open topics in model predictive control. The first is the performance of model predictive control methods under the influence of disturbances. Presented here is a result concerning the stability of model predictive control in the presence of an exponentially stable disturbance. The second concerns the use of model predictive control for stochastic systems. This paper presents a comparison of several different optimization-based control strategies as benchmarks for the performance of model predictive control. Techniques examined include dynamic programming, open-loop optimal control and certainty equivalence control.

The stability of constrained receding horizon control with state estimation

A stable, constrained, receding horizon, state feedback regulator combined with a stable state estimator is presented and shown to be asymptotically stable. The regulator is a discrete time, infinite horizon formulation that allows the incorporation of both state and input constraints. The state estimator is any stable discrete time linear observer.

Dynamic programming and model predictive control

Presents a criterion for assessing the stability of nonlinear model predictive control (MPC). The criterion is based on the monotonicity of the MPC cost function as a function of horizon length, and is derived using dynamic programming theory in a deterministic setting.

Feedback Through Steady-State Target Optimization for Nonlinear Model Predictive Control

Model predictive control (MPC) algorithms use an explicit process model to predict future plant behavior and select an optimal control sequence based on a user-defined objective function. The optimal sequence is implemented until new data are available, at which time the data are incorporated as feedback and the calculation is repeated. One of the defining features of MPC is the repeated optimization of an objective that incorporates the most recent feedback from the process. Since most MPC algorithms used in industry are based on input-output models, state feedback is rarely used in practice. Feedback is usually incorporated by including an output error term in the objective function that includes the effects of disturbances and model mismatch. When internal states are included in the process model, other feedback options become available. This paper presents a promising new feedback approach in which the output error term is used to precalculate steady-state targets for state and control variables by means of an initial nonlinear program. The target values are then used to formulate the dynamic MPC objective. Results show that the new approach can provide stability and robustness properties equivalent to those of conventional MPC feedback formulations, with as much as an order of magnitude decrease in overall computation time. This makes nonlinear, state-based MPC much more attractive for on-line implementation.

Implementable model predictive control in the state space

Model predictive control is an optimal control based method for constrained feedback control. Previous work at The University of Texas at Austin has focussed on the development of model predictive controllers that are nominally asymptotically stable for all valid tuning parameters. This development eliminated the need for tuning to obtain nominal stability. However, some implementation issues were not addressed. This work provides a discussion of those issues and solutions that allow the application of a nominally stable linear model predictive controller to be more easily realized in practice. The algorithms discussed in this work are implemented using Octaves (1993) high level interactive language and can be easily translated into other programming languages.

Model Identification and Control of A Semibatch Chemical Reactor

Two consecutive, irreversible chemical reactions are conducted in an isothermal, liquid-phase, semibatch chemical reactor. To drive the reactions forward, a strong base is added. Overaddition of base results in total loss of batch. A controller is desired for addition of base that will achieve high conversion in minimum time without overshooting the endpoint. The controller is derived as the solution of a nonlinear programming problem. To prevent overshoot despite model parameter uncertainty, the nonlinear program enforces constraints not only on the predicted states but on an estimate of state uncertainty at the final time.