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 synergetic control design methodology turns out to be closely related to the methods of variable structure sliding mode control. In fact, the method of sliding surface design from the sliding mode control are essential for designing similar 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 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 (LQR) approach by solving the associated Riccati equation.

Volume Subject Area:
Dynamic Systems and Control
Topics:
Control equipment, Sliding mode control, Design, Design methodology, Differential equations, Manifolds, Optimal control, Variational techniques
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