Moving horizon strategies for the constrained monitoring and control of nonlinear discrete-time systems.

摘要

The rational design of process monitoring and control systems requires the solution of dynamic programs. With a few notable exceptions, dynamic programs are difficult, if not impossible, to solve, as the computational complexity scales exponentially in the problem dimensions. One approximate strategy that circumvents the computational difficulties associated with dynamic programming while still retaining many desirable properties is the moving horizon approximation. Moving horizon approximations are optimization based strategies that approximate the dynamic program with a series of open-loop optimal control problems. Unlike other strategies, moving horizon approximations can handle explicitly nonlinear differential algebraic equations and inequality constraints. In this dissertation, we investigate the moving horizon approximation for the constrained process monitoring (moving horizon estimation) and control (model predictive control) of nonlinear discrete-time systems. A framework is proposed for analyzing the stability properties of the moving horizon approximation. This framework allows us to derive sufficient conditions for stability and propose practical algorithms for online implementation.; In addition to the theoretical results, practical issues regarding constraints, computation, and robustness are studied. We discuss issues regarding inequality constraints in process monitoring. By incorporating prior knowledge in the form of inequality constraints, one can significantly improve the quality of state estimates for certain problems. We demonstrate how inequality constraints provide a flexible tool for complementing process knowledge and a strategy also for model simplification. For control, techniques are developed for handling inequality constraints active at steady state. Computational issues are addressed. Stable suboptimal algorithms for constrained estimation and control are proposed that do not require an optimal solution: rather, a feasible solution suffices. Issues related to formulating model predictive control as a linear program are discussed. A computationally efficient interior point algorithm is developed for the model predictive control of large process systems. The issue of output feedback and robustness are addressed by formulating MPC as a dynamic game. The game formulation allows us to obtain a separation for output feedback and prove that the closed-loop system has finite gain. These results are extremely conservative, however, and limitations of the proposed strategy are discussed.