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A failure-prone manufacturing system with random part processing time and random product demand is considered. The optimal control policy is derived by formulating the process as a discrete-state Markovian decision process using uniformization technique. It is shown that the optimal policy is of a switching-curve control. Neural-network is used to get the function of such switch-curve.
This paper is the second in a series of two dealing with the spatial optimization of the heat exchanger temperature profiles of exothermic tubular reactors under the assumption of steady-state and plug flow characteristics. The minimum principle of Pontryagin (optimal control theory) is applied in a straightforward, analytical sense. To enable a trade-off between process performance and global heat...
The open loop optimal control (dynamic optimization) of distributed parameter systems is considered here. These problems are usually solved by the Control Vector Parameterization (CVP) approach, which transforms the original dynamic optimization method into an outer nonlinear programming problem, which requires the solution of an inner initial value problem (IVP). The solution of this IVP (set of...
This series of two papers deals with the spatial optimization of the heat exchanger temperature profile of an exothermic tubular reactor under the assumption of steady state and plug flow characteristics. The minimum principle of Pontryagin (optimal control theory) is applied in a straightforward, analytical sense. To enable a trade-off between process performance and heat loss a combined cost criterion...
The problem of controlling a near-Hamiltonian noisy system so as to prevent it from overcoming the potential barrier is considered. An exponential risk-sensitive residence time criterion is examined as a solution of a related HJB equation. The averaged HJB equation is constructed as a first order PDE with the coefficients dependent on the noise intensity in the leading order term, though this intensity...
Nonlinear optimal control problems, in which state trajectories are permitted to be discontinuous at a finite number of times, and the jump times are choice variables, are analysed. Problems such as these arise in economics, lazer technique, and robototechnique. Necessary conditions for optimality, in the form of a Maximum Principle, for the impulse optimal control problems with general terminal and...
In many applications of motion control, problems associated with imprecisely measured or changing load (mass or moment of inertia) constitute a serious obstacle in the design of satisfactory controlling systems, more and more often compelling the introduction of various forms of uncertainties to engineering solutions. This paper deals with the time-optimal control for mechanical systems with uncertain...
In this paper we consider the problem of minimizing the H∞-norm of the sum of two systems which are interconnected with two different controller components. We sketch two specific applications of this decentralized control problem. As the main contribution, we reveal that this structured controller design problem admits a full LMI solution if only one of the systems in the interconnection obeys a...
The continuously increasing daily traffic congestions on motorway networks call for innovative control measures that would drastically improve the current traffic conditions. Mainstream traffic flow control (MTFC) is proposed as a novel motorway traffic management tool. Its possible implementation and principal impact on traffic flow efficiency is analysed. Variable speed limits, suitably operated...
In this paper, we propose a universal control formula with local LQ performance for feedback linearizable systems. We show the inverse optimality and the gain margin of the proposed controller. The proposed controller provides an easy transformation method from a local LQ controller to the nonlinear inverse optimal controller. The effectiveness of the proposed method is confirmed by experiments of...
An optimal tracking controller design approach for non-linear non minimum-phase systems based on the concept of modified optimal control is presented. We extend the existing design strategy of modified optimal control to non-linear time-variant systems, since tracking a desired trajectory results in a time-variant non-linear system for the tracking error. We obtain an optimal control law which achieves...
The optimal linear-quadratic controller problem is treated for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations. As a result, the optimal controller equations are obtained in both cases, including the linear equation for the optimally controlled minmax estimate and two Riccati equations for the...
Finite-time optimal control problems with quadratic performance index for linear systems with linear constraints can be transformed into Quadratic Programs (QPs). Model Predictive Control requires the online solution of such QPs. This can be obtained by using a QP solver or evaluating the associated explicit solution. Objective of this note is to shed some light on the complexity of the two approaches.
Solving optimal control problems for spatially-distributed systems with multiple spatial dimensions can be computationally expensive. A numerical algorithm is proposed that combines a radial basis function expansion for the target trajectory with moment analysis. The approach is applicable to optimal control problems for linear spatially-distributed systems, for which the solution is expressed as...
This work considers efficient methods for the optimal control of a bilinear distributed parameter system representing the evolution of a scalar field in a fluid flow. The aim is to influence the flow field in order to maximize fluid mixing. The cost by which performance is judged is the ‘mix-norm’ defined in Mathew, Mezic and Petzold (Physica D 2005). The problem is particularly challenging as a large...
This paper attempts to provide a tutorial mode presentation of a time-optimal transfer problem in the geometric framework. The control objective is to change both the orientation and position of a ball sandwiched between two plates in minimum time. The lower plate is fixed and the upper plate can be actuated in two lateral directions. In the geometric framework, the problem of time-optimal reorientation...
A novel optimal control algorithm incorporating a cost structure implied by quantity discounts is applied to a differential equation model of an inventory system. Rather than using a demand forecast, this approach is intended to regulate the system in real time in response to inventory variations. Some examples illustrate how the system response is generated and how it is affected by quantity discounts...
This paper develops a necessary and sufficient condition for the following relationship to exist between two given uncertain systems defined in terms of IQCs: Every input-output behaviour of the first uncertain system is an input-output behaviour of the second uncertain system.
A smooth trajectory generator useful in motion control systems is presented. The considered generator is a second order nonlinear system which receives as input a standard reference signal (step, ramp, etc.) and provides as output a smooth reference signal satisfying proper nonlinear constraints on the state variables as, for example, bounds on the first time-derivative x of the output x, or bounds...
A general question one has to face in the study of an optimal control problem is the representation of the closure of the set of trajectories. Loosely speaking, two main problems lie at the basis of the non triviality of this question: the lack of sufficient convexity assumptions (which is at the origin of the introduction of the so-called chattering controls) and the occurrence of unbounded controls...
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