It is possible to construct [L.sub.2] gain if a Hamilton-Jacobi-Isaacs (HJI) equation can be solved 6]. Aliyu, "An approach for solving the Hamilton-Jacobi-Isaacs equation (HJIE) in nonlinear [H.sub.[infinity]] control," Automatica, vol. Transformation of CLF to ISS-CLF for nonlinea...
Second, the corresponding constrained Hamilton-Jacobi-Isaacs (HJI) equation is formulated, and then the quasi L 2 -gain analysis of the nonlinear system is employed. Third, an iterative algorithm based on the game theoretic interpretation of the generalized HJI (GHJI) equation by using neural ...
An iterative computationally efficient solution technique based on the game theoretic interpretation of the HJI equation is presented. The relation between attenuation gain and the region of asymptotic stability of the H∞ controller is discussed from the game theoretic perspective. The solution is ...
This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions.doi:10.1007/s002459900096P. SoraviaSpringer-VerlagApplied Mathematics & Optimization...
An algorithm is presented for computing the reachable set of a dynamic system. The algorithm is based on a proof that the reachable set is the zero sublevel set of the viscosity solution of a particular time-dependent Hamilton-Jacobi-Isaacs partial differential equation (HJI PDE). We implement ...
This is well known for linear systems, using the Riccati equation instead of the HJI equation. We do this using the theory of differential games and viscosity solutions.SoraviaP.EBSCO_AspApplied Mathematics & OptimizationP. Soravia: Equivalence between nonlinear H∞ control problems and existence ...
To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also ...
The inequality version of HJI equation , as mentioned in Equation (A4) in Lemma A1 of Appendix A.5, is −∂𝑉1(𝒙∗(𝑡),𝑡)∂𝑡≤∂𝑉1(𝒙∗,𝑡)∂𝒙∗𝒙∗˙+𝒓𝑲𝑇𝒓𝑲−𝛼2𝛏𝑇𝜉 (26) Remark 6. The derivation for 𝐻∞ ...