The quasi-norm allows using nonquadratic supply rates along with dissipativity theory to formulate the robust optimal control problem using Hamilton-Jacobi-Isaacs (HJI) equations. An iterative computationally efficient solution technique based on the game theoretic interpretation of the HJI equation is ...
In this paper we extend to completely general nonlinear systems the result stating that the $ {{\cal H}}_\infty $ suboptimal control problem is solved if and only if the corresponding Hamilton—Jacobi—Isaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear ...
In this chapter, we propose a new algorithm to solve Riccati equations and certain Hamilton—Jacobi—Bellman—Isaacs (HJBI) equations arising in $$H_{\infty}$$...
The quasi-norm allows using nonquadratic supply rates along with the theory of dissipative systems to formulate the robust optimal control problem for constrained input systems using the Hamilton-Jacobi-Isaacs (HJI) equation. Hence, the constrained optimal control problem is formulated as a closely ...
P. Soravia: Equivalence between nonlinear H∞ control problems and existence of viscosity solutions of Hamilton-Jacobi-Isaacs equations, Appl. Math. Optim. 39 (1999), no. 1, 17- 32.P. Soravia, Equivalence between nonlinear H∞ control problems and ex- istence of viscosity solutions of ...
The method is easily extended to the Hamilton-Jacobi-Isaacs (HJI) PDE. Software is available on the web to compute local approximtate solutions of HJB and HJI PDEs. [References: 23]Krener AJ.SIAM Journal on Control and OptimizationA. J. Krener. The local solvability of a hamilton-jacobi...
Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are, respectively, used to compute the value function and the optimal control fo...