Ravi Gondhalekar

Least restrictive move-blocking model predictive control

Abstract The authors recently proposed an approach to enforce strong feasibility in move-blocking model predictive control problems. In this paper the approach is utilized to design strong model predictive control problems which generate least restrictive controllers. The domains of different move-blocking regimes are thus equal and the same as the non-moveblocking maximum. This allows comparison of different move-blocking regimes based on cost performance only, without considering domain size also. A numerical example and case study demonstrate that between input- and offset-move-blocking, the latter is generally superior.

Strong feasibility in input-move-blocking model predictive control

Abstract Time-invariant input-move-blocking regimes are used in many practical online model predictive control systems in order to reduce the computational complexity of the associated finite-horizon optimal control problem, and have been shown to be beneficial for offline model predictive control methods also. However, until now there exists no method to ensure strong feasibility. In this paper a least-restrictive method to enforce strong feasibility in time-invariant input-move-blocking model predictive control problems is proposed, where the state of the first prediction step is constrained to a novel type of controlled invariant set, called here a controlled invariant feasible set. An algorithm to determine maximal controlled invariant feasible sets is proposed. This algorithm is shown to be semi-decidable for the case of linear, time-invariant plants with time-invariant, polytopic state and control input constraint sets.

Non-linear prediction horizon time-discretization for model predictive control of linear sampled-data systems

Model predictive sampled-data control of linear continuous-time plants is considered. The time-discretization of the prediction horizon may be non-linear, in order to reduce the number of optimization variables for a given prediction horizon length. This is done for the purpose of allowing faster implementation. While the method is aimed at constrained systems, this paper focuses on the achievable performance of such control strategies for unconstrained systems. A general solution to the finite-horizon optimal control problem is derived for a prediction horizon of arbitrary time-discretization. The model predictive control strategy is consequently derived, and the optimal control input shown to be given by a time-invariant state feedback expression. Three non-linear prediction horizon time-discretization schemes are proposed, and their relative merits discussed. The benefit of employing the presented control strategy is demonstrated by a satellite attitude control case study. The same case study is further used to highlight limitations of and performance differences between the three proposed prediction horizon time-discretization schemes.

Recursive feasibility guarantees in move-blocking MPC

A method for enforcing recursive feasibility in time-invariant offset-move-blocking MPC schemes is proposed. The method constrains the state at the first prediction step to a controlled invariant feasible set, introduced recently by the authors for enforcing recursive feasibility in input-move- blocking MPC. Two algorithms for the determination of maximal controlled invariant feasible sets are presented. In the case of stabilizable, linear, time-invariant plants with time-invariant, polytopic constraints, both algorithms are semi-decidable. In situations where using one algorithm alone does not lead to decidability, both algorithms can be used together to determine a controlled invariant feasible under-approximation of the maximal controlled invariant feasible set to arbitrary accuracy.

Performance and stability analysis of discontinuous PWA systems by piecing together PWQ functions

Abstract An algorithm for evaluating the cost performance of discontinuous autonomous discrete-time piecewise affine systems is presented. The algorithm performs reverse reachability analysis and constructs a piecewise quadratic trajectory cost function over the entire region of attraction of the origin while explicitly taking into account the exact spatial evolution of the trajectories and the exact switching structure of the system as a whole. Available explicitly, this cost function can be integrated in order to evaluate the cost performance of the entire system. The reverse reachability algorithm is applied to the problem of constructing Lyapunov functions. The resulting Lyapunov functions are less conservative than other forms of Lyapunov function commonly used for stability analysis of autonomous discrete-time piecewise affine systems.