Nonlinear approximate game-theoretic estimation and control

A game-theoretic approach to nonlinear estimation and control synthesis and analysis is proposed. Two classes of nonlinear dynamical systems are considered, namely, linear dynamical systems with nonlinear ordinary perturbation with respect to a small parameter ;Next, for a class of modifiable nonlinear dynamical systems, both stable nonlinear game-theoretic filters and controllers, which solve the disturbance attenuation problems, are obtained with a dissipative approach. Then, sufficient conditions to render the dissipative inequalities satisfied with respect to the worst linear strategies for the process and sensor disturbances are derived. Both internal stability and disturbance attenuation properties are implied by the dissipativity for both estimation and control problems.;Subsequently, the game-theoretic approach is applied to derive both continuous-time and discrete-time decentralized filters. The continuous-time version of the dentralized estimator is determined from a disturbance attenuation problem which requires the solution to a deterministic differential game. The discrete-time form of the decentralized estimator is derived from a stochastic optimization problem minimizing with respect to the estimate the cost criterion of the expected value of the exponential of the sum of the squares of estimation errors at each stage time subject to a Gauss-Markov system. The essential property of this decentralized filter is that the computation of locally processed data which includes the local state estimate at a node of a K node interconnected network can be transmitted and combined at any time to produce the best global state estimate given all the data in the network. This decomposition generalizes the results of the decentralized Kalman filter. Finally, numerical examples illustrate the approximate nonlinear filter and controller performance.