Variance-Constrained Multi-Objective Stochastic Control and Filtering

Chapter 11Mixed H₂/H_∞ Control with Randomly Occurring Nonlinearities: The Finite-Horizon Case

As the stochastic systems have been playing more and more important roles in control theory and applications, a special case of the multi-objective design problem, the mixed control and filtering for stochastic systems have recently stirred much research interest and some initial results have been available in the literature. Several analysis and design methods including the linear matrix inequality approach and game theory strategy have been developed for such a problem and have made a significant impact to both theoretical advance and practical application of the mixed H₂/H_∞ control and filtering for linear stochastic systems. Nevertheless, when it comes to the nonlinear stochastic system, the reported results are relatively fewer due mainly to the complicated dynamics of the nonlinearities. Moreover, most of the existing literature has focused on the time-invariant nonlinear stochastic systems despite the fact that real-world systems are usually time-varying, that is, all the system parameters are explicitly dependent on time. In fact, for a truly time-varying nonlinear stochastic system, we would be more interested in the transient behaviors over a finite time-interval, e.g., the mixed performance over a finite horizon. Unfortunately, for time-varying stochastic nonlinear systems, ...