Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A deterministic optimal control problem is solved for a control-affine non-linear system with a non-quadratic cost function.  algebraically solve the Hamilton–Jacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton–Jacobi partial differential equation.  interpret the value function in terms of the control Lyapunov function. Then  provide the stabilizing controller and the stability margins. Furthermore,  derive an optimal controller for a control-affine non-linear system using the state dependent Riccati equation (SDRE) method; this method gives a similar optimal controller as the controller from the algebraic method.  also find the optimal controller when the cost function is the exponential-of-integral case, which is known as risk-sensitive (RS) control. Finally,  show that SDRE and RS methods give equivalent optimal controllers for non-linear deterministic systems. Examples demonstrate the proposed methods.
['Chang-Hee Won', 'Saroj Biswas']
I am writing a research paper on a idea Optimal control using an algebraic method for control-affine non-linear systems
[{"from": "human", "value": "I am writing a research paper on a idea Optimal control using an algebraic method for control-affine non-linear systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A deterministic optimal control problem is solved for a control-affine non-linear system with a non-quadratic cost function.  algebraically solve the Hamilton\u2013Jacobi equation for the gradient of the value function. This eliminates the need to explicitly solve the solution of a Hamilton\u2013Jacobi partial differential equation.  interpret the value function in terms of the control Lyapunov function. Then  provide the stabilizing controller and the stability margins. Furthermore,  derive an optimal controller for a control-affine non-linear system using the state dependent Riccati equation (SDRE) method; this method gives a similar optimal controller as the controller from the algebraic method.  also find the optimal controller when the cost function is the exponential-of-integral case, which is known as risk-sensitive (RS) control. Finally,  show that SDRE and RS methods give equivalent optimal controllers for non-linear deterministic systems. Examples demonstrate the proposed methods."}]