A unification between nonlinear-nonquadratic optimal control and integrator backstepping

✍ Scribed by Wassim M. Haddad; Jerry L. Fausz; Vijaya-Sekhar Chellaboina; Chaouki Abdallah

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 217 KB
• Volume: 8
• Category: Article
• ISSN: 1049-8923
• DOI: 10.1002/(sici)1099-1239(199808)8:10<879::aid-rnc351>3.0.co;2-0

✦ Synopsis

In this paper we develop an optimality-based framework for backstepping controllers. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping controllers parametrized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system and thus guarantees both optimality and stability. The results are specialized to the cases of integrator backstepping and block backstepping for cascade systems with linear and nonlinear input subsystems.