We consider the problem of internal regional controllability with output constraints. It consists in steering a hyperbolic system to a final state between two prescribed functions only on a subregion of the evolution system domain. This problem is solved by characterizing the optimal control in terms of a subdifferential associated with the minimized functional.
In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as...
Mathematics Subject Classification: 26A33; 93C15, 93C55, 93B36, 93B35, 93B51; 03B42; 70Q05; 49N05This paper proposes a novel method to design an H∞ -optimal fractional order PID (FOPID) controller with ability to control the transient, steady-state response and stability margins characteristics. The method uses particle swarm optimization algorithm and operates based on minimizing a general cost function. Minimization of the cost function is carried out subject to the H∞ -norm; this norm is also...
A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear...
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In...
In this paper we present a robust real-time optimization method for the online linear oil blending process. The blending process consists in determining the optimal mix of components so that the final product satisfies a set of specifications. We examine different sources of uncertainty inherent to the blending process and show how to address this uncertainty applying the Robust Optimization techniques. The polytopal structure of our problem permits a simplified robust approach. Our method is intended...
A previous paper by the same authors presented a general theory solving (finite horizon) feasibility and optimization problems for linear dynamic discrete-time systems with polyhedral constraints. We derived necessary and sufficient conditions for the existence of solutions without assuming any restrictive hypothesis. For the solvable cases we also provided the inequative feedback dynamic system, that generates by forward recursion all and nothing but the feasible (or optimal, according to the cases)...
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...
For a problem of optimal discrete control with a discrete control set composed of vertices of an n-dimensional permutohedron, a fully polynomial-time approximation scheme is proposed.
In this article we consider a control system modelling a batch reactor in which three species X1, X2, X3 are reacting according to the scheme X1 → X2 → X3, each reaction being irreversible. The control is the temperature T of the reactions or the derivative of this temperature with respect to time. The terminal constraint is to obtain a given concentration of the product X2 at the end of the batch. The objective of our study is to introduce and to apply all the mathematical tools to compute the...