This paper deals with the paradigm of controlling uncertain stochastic systems for which control and state variations increase uncertainty (CSVIU). The discrete time CSVIU model is particularly useful when an accurate...
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This paper deals with the paradigm of controlling uncertain stochastic systems for which control and state variations increase uncertainty (CSVIU). The discrete time CSVIU model is particularly useful when an accurate dynamic model is unattainable, and only a rough model is available. Interesting features arise from the optimal control solution for the model. In particular, the optimal control action is to remain idle within a certain region of the state space - the inaction region. This feature, peculiar to the CSVIU approach, has ties to cautionary control policies found in economics. The convexity of the cost function holds for the discounted control problem with quadratic costs when the noise is Gaussian, and the control policy admits a solution in closed form in some regions of the state space. A linearly perturbed Lyapunov equation inside the inaction region, and a rational Riccati equation, asymptotically in far-off regions, characterize the control. We show the stochastic stability of solutions and provide numerical experiments that underline CSVIU model control's interesting peculiarities. (c) 2020 Elsevier Ltd. All rights reserved.
This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. Accord...
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This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system's state is augmented with disturbances and transformed into a new coordinate framework. based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system. (C) 2020 Elsevier Ltd. All rights reserved.
We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance in data, we have that a set of ...
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We address the problem of designing a stabilizing closed-loop control law directly from input and state measurements collected in an experiment. In the presence of a process disturbance in data, we have that a set of dynamics could have generated the collected data and we need the designed controller to stabilize such set of data-consistent dynamics robustly. For this problem of data-driven control with noisy data, we advocate the use of a popular tool from robust control, Petersen's lemma. In the cases of data generated by linear and polynomial systems, we conveniently express the uncertainty captured in the set of data-consistent dynamics through a matrix ellipsoid, and we show that a specific form of this matrix ellipsoid makes it possible to apply Petersen's lemma to all of the mentioned cases. In this way, we obtain necessary and sufficient conditions for data-driven stabilization of linear systems through a linear matrix inequality. The matrix ellipsoid representation enables insights and interpretations of the designed control laws. In the same way, we also obtain sufficient conditions for data-driven stabilization of polynomial systems through alternate (convex) sum-of-squares programs. The findings are illustrated numerically.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
In this paper, we propose a continuous-time adaptive feedback controller for the optimal control of input-state-output port-Hamiltonian systems with respect to general Lagrangian performance indices. The proposed cont...
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In this paper, we propose a continuous-time adaptive feedback controller for the optimal control of input-state-output port-Hamiltonian systems with respect to general Lagrangian performance indices. The proposed control law implements an online learning procedure which uses the Hamiltonian of the system as an initial value function candidate. The continuous-time learning of the value function is achieved by means of a certain Lagrange multiplier that allows to evaluate the optimality of the current solution. In particular, constructive conditions for stabilizing initial value function candidates are stated and asymptotic stability of the closed-loop equilibrium is proven. Simulations of an exemplary nonlinear optimal control problem demonstrate the performance of the controller resulting from the proposed online learning procedure. (C) 2021 Elsevier Ltd. All rights reserved.
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