A class of nonlinear game-theoretic filters and controllers using a dissipative approach

Abstract

For a class of nonlinear time-varying systems, a stable nonlinear game-theoretic filter (GTF), which solves the disturbance attenuation problem, is obtained with a dissipative approach. For such nonlinear functions (modifiable nonlinearities), the estimation error propagates almost linearly. A sufficient condition to render the dissipative inequality satisfied for the GTF with respect to the worst strategy for the process and sensor disturbances is derived. The filter gain is obtained from a Riccati differential equation (RDE) which results from bounding the dissipative inequality. The design parameters are then scaling coefficients multiplying the weighting matrices in the RDE. Then, a sufficient condition for the GTF to be asymptotically stable is derived and shown to be sufficient for the GTF to be dissipative. The disturbance attenuation property is implied by the dissipativity of the GTF. Next, for a class of dynamical system with modifiable nonlinear measurement functions but linear dynamics, an implementable stabilizing time-varying, nonlinear game-theoretic controller (GTC) is derived by bounding the dissipative inequality of the feedback control. Its structure is assumed from a natural modification, to accommodate the modifiable nonlinearity, of the corresponding linear quadratic game problem. Sufficient conditions for dissipativity and internal stability are obtained provided two coupled RDE are satisfied. These RDEs are somewhat modified from those obtained from the corresponding linear quadratic problem. >