1,926 research outputs found
Singular nonlinear H∞ optimal control problem
The theory of nonlinear H∞ of optimal control for affine nonlinear systems is extended to the more general context of singular H∞ optimal control of nonlinear systems using ideas from the linear H∞ theory. Our approach yields under certain assumptions a necessary and sufficient condition for solvability of the state feedback singular H∞ control problem. The resulting state feedback is then used to construct a dynamic compensator solving the nonlinear output feedback H∞ control problem by applying the certainty equivalence principle
Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty
The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward H∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation
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Robust H2/H∞-state estimation for systems with error variance constraints: the continuous-time case
Copyright [1999] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.The paper is concerned with the state estimator design problem for perturbed linear continuous-time systems with H∞ norm and variance constraints. The perturbation is assumed to be time-invariant and norm-bounded and enters into both the state and measurement matrices. The problem we address is to design a linear state estimator such that, for all admissible measurable perturbations, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞ norm upper bound constraint, simultaneously. Existence conditions of the desired estimators are derived in terms of Riccati-type matrix inequalities, and the analytical expression of these estimators is also presented. A numerical example is provided to show the directness and effectiveness of the proposed design approac
Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey
The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H ∞ control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out
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