On output feedback nonlinear model predictive control using high gain observers for a class of systems

Abstract

In recent years, nonlinear model predictive control schemes have been derived that guarantee stability of the closed loop under the assumption of full state information. However, only limited advances have been made with respect to output feedback in connection to nonlinear predictive control. Most of the existing approaches for output feedback nonlinear model predictive control do only guarantee local stability. Here we consider the combination of stabilizing instantaneous NMPC schemes with high gain observers. For a special MIMO system class we show that the closed loop is asymptotically stable, and that the output feedback NMPC scheme recovers the performance of the state feedback in the sense that the region of attraction and the trajectories of the state feedback scheme are recovered for a high gain observer with large enough gain and thus leading to semi-global/non-local results.

Output Feedback Nonlinear Predictive Control -a Separation Principle Approach

“…In comparison to (Imsland et al 2001b) we derive results for the sampled case, i.e. we do not assume that the state feedback is continuously recalculated.…”

State and Output Feedback Nonlinear Model Predictive Control: An Overview

“…In [43,44] it was shown that based on the results of [5,85], semi-global practical stability results could be obtained for instantaneous NMPC based on a special class of continuous-time models, using high gain observers for state estimation. In this context, semi-global practical stability means that for any compact region inside the state feedback NMPC region of attraction, there exists a sampling time and an observer gain such that for system states starting in this region, the closed loop take the state into any small region containing the origin.…”

Integration of Real-time Optimization & and Model Predictive Control

“…The first phase deals with generating a state trajectory that optimizes a given objective function while respecting the system dynamics and constraints, and the second phase deals with the design of a controller that would regulate the system around a specific setpoint. At each sampling instant, the current value of the setpoint, x r ðt;ĥÞ given by the extremum-seeking setpoint update (16) is passed down to the tracking controller for implementation. The approach can be viewed as a sampling and zero-hold implementation of the setpoint update law.…”

“…Since the true optimal setpoint depends on h, the actual desired trajectory x à r ðt; hÞ is not available in advance. However, x r ðt;ĥÞ can be generated from the setpoint update law (16) and the corresponding reference input u r (x r ) can be computed online. Formally, this assumption requires invertibility and hence, strong relative degree, of the nonlinear system (2).…”

“…For ease of presentation, only the full state information case is considered. The design of an output feedback approach can be achieved using output feedback MPC techniques [16,13,2]. Note that the work presented in [5] provides an initial study of the class of problems treated in this paper for linear control systems.…”