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A new class of state dependent parametrizations is introduced which can be used in linear model predictive control (MPC) to approximate the optimal predicted input trajectories and thereby speed up the online optimization. The parametrizations are piecewise constant over the state space and also contain, in addition to previous results, a piecewise linear state feedback term. A new data mining algorithm...
In this work, we discuss normal forms of necessary conditions of optimality (NCO) for optimal control problems subject to pathwise state constraints and for problems in the calculus of variations with inequality constraints. It is known that standard forms of the NCO may fail to provide information that is useful to identify optimal solutions, namely when the multiplier associated with the objective...
We consider a network of control systems connected over a graph. Considering the graph structure as constraints on the set of permissible controllers, we show that such systems are simply constrained by a certain sparsity pattern. We provide conditions for which such systems are well-posed, and, under the appropriate assumptions, we show that such systems are quadratically invariant. This allows for...
In this paper we use bilevel programming to find the maximum difference between a reference controller and a low-complexity controller in terms of the infinity-norm difference of their control laws. A nominal MPC for linear systems with constraints, and a robust MPC for linear systems with bounded additive noise are considered as reference controllers. For possible low-complexity controllers we discuss...
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the controller to the structure of the plant. In this paper, we consider the problem of finding the closest subset and superset of the decentralization constraint which are...
This paper presents simulation studies on the optimal energy control of an inverter-fed three-phase induction motor (1 hp). An overview of various controllers: loss model controller, search controller and their hybridization are given. Induction motor parameter variations due to temperature rise and core saturation are considered when loss models are derived. Mine hoist drive of a mineral industry...
Deterministic long run average optimal control problems and, in particular, periodic optimization problems are related to certain infinite-dimensional linear programming (LP) problems, which can be approximated by finite-dimensional LP problems. In this paper we study problems dual to these infinite- and finite- dimensional LP problems, and we investigate a possibility of using solutions of the latter...
The Riemannian exponential map on a noncompact Lie Group, which is determined by a Riemannian metric, is different from the Lie group exponential map determined by one-parameter subgroups. The Riemannian exponential map which represents the geodesic of the optimal transformation is obtained in terms of the minimal geodesic equation on SL(n, R). Generally, the Newton optimization method on Lie group...
This paper is concerned with the problem of receding horizon control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution. Moreover, under the assumption that the zero-input...
We consider the design of optimal static feedback gains for interconnected systems subject to architectural constraints on the distributed controller. These constraints are in the form of sparsity requirements for the feedback matrix, which means that each controller has access to information from only a limited number of subsystems. We derive necessary conditions for the optimality of structured...
A problem of optimal control of Markov chain with finite state space is considered. We consider a non-stationary finite horizon problem with constraints, given as a set of inequalities. Basing on recent results on existence of optimal solution we suggest to use the dual approach to optimization and thereby an approach to effective numerical algorithms. The approach is illustrated by numerical examples.
A method is presented to integrate a complete ??black-box?? error correction scheme, that takes quantum process tomography as input and iterates the control until it finds an optimal error correcting encoding and recovery.
The optimal control problem of multiple conveyor-serviced production station (CSPS) system is concerned, and the objective is to maximize the part-processing rate of the entire system by choosing a coordinate look-ahead control strategy for each station. According to the idea of event-based optimization, and by using the concept of performance potentials, an event-based Q-learning algorithm is proposed...
Model predictive control (MPC) is an on-line control technique originally developed for slow processes which makes an assessment between input effort and output error while respecting constraints on inputs and outputs. Due to improved computing power and algorithms, MPC is nowadays also applied to mechatronic systems. For these systems, achieving minimal settling time is the main concern, while the...
In this paper, we prove the optimality of disturbance-affine control policies in the context of one-dimensional, box-constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax (worst-case) objective, and convex state costs plus linear control costs. Our proof methodology, based on techniques from polyhedral geometry, is elegant and conceptually simple, and...
In practice, the convergence rate and stability of perturbation based extremum-seeking (ES) schemes can be very sensitive to the curvature of the plant map. This sensitivity arises from the use of a gradient descent adaptation algorithm. Such ES schemes may need to be conservatively tuned in order to maintain stability over a wide range of operating conditions, resulting in slower optimisation than...
We regard a network of coupled nonlinear dynamical systems that we want to control optimally. The cost function is assumed to be separable and convex. The algorithm we propose to address the numerical solution of this problem is based on two ingredients: first, we exploit the convex problem structure using a sequential convex programming framework that linearizes the nonlinear dynamics in each iteration...
The problem of receding horizon control for a class of nonlinear distributed processes is investigated. The main focus of the manuscript lies in the development of a computationally efficient method to identify the optimal control action with respect to predefined performance criteria. An optimal control problem is formulated and is solved using standard, gradient-based, search algorithms. Employing...
This paper presents a novel, computationally feasible procedure for computing optimal switching surfaces, i.e. optimal feedback controllers for switched autonomous nonlinear systems. Such systems are regulated by appropriately scheduling their operation modes over time. Given a finite mode sequence, the control task is to determine switching surfaces, which implicitly encode locally optimal switching...
The objective of the standard parts optimal control problem is to find a number, m, of control inputs to a given input-output system that can be used in different combinations to achieve a certain number, n, of output objectives and to do this in such a way that a specified figure-of-merit measuring the average cost of control is minimized. The problem is especially interesting when m is significantly...
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