Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach

In order to guarantee stability, known results for MPC without additional terminal costs or endpoint constraints often require rather large prediction horizons. Still, stable behavior of closed loop solutions can often be observed even for shorter horizons. Here, we make use of the recent observation that stability can be guaranteed for smaller prediction horizons via Lyapunov arguments if more than only the first control is implemented. Since such a procedure may be harmful in terms of robustness, we derive conditions which allow to increase the rate at which state measurements are used for feedback while maintaining stability and desired performance specifications. Our main contribution consists in developing two algorithms based on the deduced conditions and a corresponding stability theorem which ensures asymptotic stability for the MPC closed loop for significantly shorter prediction horizons.Comment: 6 pages, 3 figure

Adaptive model predictive control

The problem of model predictive control (MPC) under parametric uncertainties for a class of nonlinear systems is addressed. An adaptive identi er is used to estimate the pa- rameters and the state variables simultaneously. The algorithm proposed guarantees the convergence of parameters and the state variables to their true value. The task is posed as an adaptive model predictive control problem in which the controller is required to steer the system to the system setpoint that optimizes a user-speci ed objective function. The technique of adaptive model predictive control is developed for two broad classes of systems. The rst class of system considered is a class of uncertain nonlinear systems with input to state stability property. Using a generalization of the set-based adaptive estimation technique, the estimates of the parameters and state are updated to guarantee convergence to a neighborhood of their true value. The second involves a method of determining appropriate excitation conditions for nonlin- ear systems. Since the identi cation of the true cost surface is paramount to the success of the integration scheme, novel parameter estimation techniques with better convergence properties are developed. The estimation routine allows exact reconstruction of the systems unknown parameters in nite-time. The applicability of the identi er to improve upon the performance of existing adaptive controllers is demonstrated. Then, an adaptive nonlinear model predictive controller strategy is integrated to this estimation algorithm in which ro- bustness features are incorporated to account for the e ect of the model uncertainty. To study the practical applicability of the developed method, the estimation of state vari- ables and unknown parameters in a stirred tank process has been performed. The results of the experimental application demonstrate the ability of the proposed techniques to estimate the state variables and parameters of an uncertain practical system.Departamento de Ingeniería de Sistemas y AutomáticaMáster en Investigación en Ingeniería de Procesos y Sistemas Industriale

Optimal Control Methods for Missile Evasion

Optimal control theory is applied to the study of missile evasion, particularly in the case of a single pursuing missile versus a single evading aircraft. It is proposed to divide the evasion problem into two phases, where the primary considerations are energy and maneuverability, respectively. Traditional evasion tactics are well documented for use in the maneuverability phase. To represent the first phase dominated by energy management, the optimal control problem may be posed in two ways, as a fixed final time problem with the objective of maximizing the final distance between the evader and pursuer, and as a free final time problem with the objective of maximizing the final time when the missile reaches some capture distance away from the evader.These two optimal control problems are studied under several different scenarios regarding assumptions about the pursuer. First, a suboptimal control strategy, proportional navigation, is used for the pursuer. Second, it is assumed that the pursuer acts optimally, requiring the solution of a two-sided optimal control problem, otherwise known as a differential game. The resulting trajectory is known as a minimax, and it can be shown that it accounts for uncertainty in the pursuer\u27s control strategy. Finally, a pursuer whose motion and state are uncertain is studied in the context of Receding Horizon Control and Real Time Optimal Control. The results highlight how updating the optimal control trajectory reduces the uncertainty in the resulting miss distance