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The main contribution of this paper is to develop a general methodology to solve a class of optimal nonlinear control problems with a single input based on a state-dependent Riccati equation. For a polynomial system of order n the paper proposes a formula for the dependence of the cost-to-go function on one of the variables, which then leads to a state-dependent Riccati equation that is linear in...
This paper develops a three degrees of freedom (DOF) PWA model for a rotorcraft MAV. To develop the PWA model, a new function approximation method using a set of linearisation points (SLP) and Voronoi partitions is proposed. The SLP method is then compared to a uniform grid (UG) approximation, which is the current method being used in the literature of PWA. Next, a PWA controller is designed so the...
This paper addresses the design of continuous-time piecewise-affine (PWA) observers for a class of nonlinear systems with sampled output. Building on observer theory for PWA systems, sufficient conditions are proposed such that a continuous-time PWA observer can be used to estimate the states of a nonlinear system linear in the input with sampled output yielding a convergent state estimation error...
This paper presents a new algorithm for piecewise affine (PWA) approximation of nonlinear systems. Such an approximation is very important to enable a reduction in the complexity of models of nonlinear systems while keeping the global validity of the models. The paper builds on previous work on PWA approximation methods, in particular on the work done by Casselman and Rodrigues, known as the Set of...
In this paper, a nonlinear optimal control problem for a third order system is defined and solved. The optimal control law is found using an inverse optimality approach to solve the Hamilton-Jacobi-Bellman equation, where the solution is obtained directly for the control input without needing to assume or compute a value function first. However, the value function can be obtained after one solves...
The main contribution of this paper is to analytically solve the Hamilton-Jacobi-Bellman equation for a class of third order nonlinear optimal control problems for which the dynamics are affine and the cost is quadratic in the input. The proposed solution method is based on the notion of inverse optimality with a variable part of the cost to be determined in the solution. One special advantage of...
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