Optimal motion control and vibration suppression of flexible systems with inaccessible outputs

This work addresses the optimal control problem of dynamical systems with inaccessible outputs. A case in which dynamical system outputs cannot be measured or inaccessible. This contradicts with the nature of the optimal controllers which can be considered without any loss of generality as state feedback control laws for systems with linear dynamics. Therefore, this work attempts to estimate dynamical system states through a novel state observer that does not require injecting the dynamical system outputs onto the observer structure during its design. A linear quadratic optimal control law is then realized based on the estimated states which allows controlling motion along with active vibration suppression of this class of dynamical systems with inaccessible outputs. Validity of the proposed control framework is evaluated experimentally

Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints

This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909, San Francisco, USA, June 29 - July 1, 201

Realizable optimal control for a remotely piloted research vehicle

The design of a control system using the linear-quadratic regulator (LQR) control law theory for time invariant systems in conjunction with an incremental gradient procedure is presented. The incremental gradient technique reduces the full-state feedback controller design, generated by the LQR algorithm, to a realizable design. With a realizable controller, the feedback gains are based only on the available system outputs instead of being based on the full-state outputs. The design is for a remotely piloted research vehicle (RPRV) stability augmentation system. The design includes methods for accounting for noisy measurements, discrete controls with zero-order-hold outputs, and computational delay errors. Results from simulation studies of the response of the RPRV to a step in the elevator and frequency analysis techniques are included to illustrate these abnormalities and their influence on the controller design

Interconnection of Discrete-Time Dissipative Systems

Strictly proper discrete-time systems cannot be passive. For passivity-based control to be exploited nevertheless, some authors introduce virtual outputs, while others rely on continuous-time passivity and then apply discretization techniques that preserve passivity in discrete-time. Here we argue that quadratic supply rates incorporate and extend the effect of virtual outputs, allowing one to exploit dissipativity properties directly in discrete-time. We derive local dissipativity conditions for a set of nonlinear systems interconnected with arbitrary topology, so that the overall network is guaranteed to be stable. For linear systems, we develop dissipative control conditions that are linear in the supply rate. To demonstrate the validity of our methods, we provide numerical examples in the context of islanded microgrids

Parameter Privacy versus Control Performance: Fisher Information Regularized Control

This article introduces and solves a new privacy-related optimization problem for cyber-physical systems where an adversary tries to learn the system dynamics. In the context of linear quadratic systems, we consider the problem of achieving a small cost while balancing the need for keeping knowledge about the model's parameters private. To this end, we formulate a Fisher information regularized version of the linear quadratic regulator with cheap cost. Here the control operator is allowed to not only control the plant but also mask its state by injecting further noise. Within the class of linear policies with additive noise, we solve this problem and show that the optimal noise distribution is Gaussian with state dependent covariance. Next, we prove that the optimal linear feedback law is the same as without regularization. Finally, to motivate our proposed scheme, we formulate an equivalent minimax problem for the worst-case scenario in which the adversary has full knowledge of all other inputs and outputs. Here, our policies are minimax optimal with respect to maximizing the variance over all unbiased estimators