Nonlinear Synergetic Optimal Controllers

Optimality properties of synergetic controllers are analyzed using the Euler-Lagrange conditions and the Hamilton-Jacobi-Bellman equation. First, a synergetic control strategy is compared with the variable structure sliding mode control. The connections of synergetic control design methodology and the methods of variable structure sliding mode control are established. In fact, the methods of sliding surface design for the sliding mode control are essential for designing invariant manifolds in the synergetic control approach. It is shown that the synergetic control strategy can be derived using tools from the calculus of variations. The synergetic control laws have a simple structure because they are derived from the associated first-order differential equation. It is also shown that the synergetic controller for a certain class of linear quadratic optimal control problems has the same structure as the one generated using the linear quadratic regulator approach by solving the associated Riccati equation. The synergetic optimal control and sliding mode control methodologies are applied to the nonlinear control of the wing-rock suppression problem. Two different wing-rock dynamic models are used to test the design of the synergetic and sliding mode controllers. The performance of the closed-loop systems driven by these controllers is analyzed and compared.