A mathematical programming approach for control of constrained nonlinear systems with uncertain parameters.

摘要

While linear control theory has been used in virtually all process control applications, the nonlinear character of many processes is becoming increasingly appreciated. However, until recently, nonlinear process control has seen relatively few results. An effort is made in this dissertation to enhance the foundation for control of general constrained nonlinear systems having process constraints, time delays, and uncertain parameters.; A nonlinear process is assumed to be modeled as a set of nonlinear ODEs. Using the duality of control theory and the theory on the solution of operator equations, the control law is developed by analogy to Newton's method. To handle the process constraints, the method is generalized to include a SQP algorithm. Both hard and soft constraints can be included in this strategy. The Hessian in the objective function is constructed to be a positive semi-definite so that global optimal QP solutions are guaranteed even though the solutions may not be unique.; The algorithm is then extended to a multistep one, i.e. the predictive time horizon consists of several steps, which parallels QDMC for linear constrained systems.; In order to deal with modelling error, the proposed control algorithm integrates with a nonlinear parameter estimator, which is called a two phase approach. In the first phase, the updated model is used by the control algorithm to predicted systems outputs and optimize the control objective. In the second phase, the recorded system output measurements are used to get an optimal set of parameters which maximizes the probability of obtaining those measured system outputs.; By treating the control algorithm as a nonlinear operator, analogies can be made to stability through contraction mappings. In addition, using the line search and choosing a large enough sampling time, a global convergence of the method can be enforced through descent properties as long as the open-loop system is asymptotically stable in the large. It is proven that the control variable constraints in the control algorithm do not destroy the descent property, which is also true when the algorithm is extended to the multistep one. (Abstract shortened with permission of author.)