This paper presents a simple approach to synthesize optimal controls from user prescribed positive definite functions. The synthesized controls minimize a user specified objective function which is a quadratic function of the control variables. The approach followed in this paper is inspired by recent developments in analytical dynamics and the observation that the Lyapunov criterion for stability of dynamical systems can be recast as a constraint to be imposed on the system. The approach used to obtain the fundamental equation of motion for constrained mechanical systems is extended to find control forces that minimize any user-specified quadratic function of the control forces while simultaneously enforcing the stability requirement as an additional constraint. This method can also be generalized to nonautonomous dynamical system described by first order nonlinear differential equations. We further explore the possibility of extending the approach to systems in which we do not have full state control.

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