Energy Control of Three Identical Pendulums under Energy Constraints

Abstract. This paper addresses the problem of energy control for three identical independent pendulums driven by a single scalar input. The objective is to asymptotically steer the energy of the first pendulum to a prescribed level while keeping those of the other two below given bounds. A penalty-type Lyapunov function combining a quadratic target term and barrier terms for the constraints is introduced. A numerically implementable explicit control law is derived based on the speed-gradient method. Additional consideration is given to the physical meaning of the basic model equations and the selective energy redistribution mechanism under a common control action. Numerical simulations are provided to confirm the convergence of the first pendulum’s energy to the target level while satisfying the imposed constraints.

Keywords: energy control, identical pendulums, speed-gradient method, penalty functions, Hamiltonian systems, numerical simulation.