Approximate and Widespread Pareto Solutions in the Structure-Control Design of Mechatronic Systems

The structure-control design approach of mechatronic systems requires a different design formulation where the mechanical structure and control system are simultaneously designed. Optimization problems are commonly stated to confront the structure-control design formulation. Nevertheless, these problems are often very complex with a highly nonlinear dependence between the design variables and performance functions. This fact has made the use of evolutionary algorithms, a feasible alternative to solve the highly nonlinear optimization problem; the method to find the best solution is an open issue in the structure-control design approach. Hence, this paper presents a mechanism to exhaustively exploit the solutions in the differential evolution (DE) algorithm in order to find more non-dominated solutions with uniformly distributed Pareto front and better trade-offs in the structure-control design framework. The proposed approach adopts an external population to retain the non-dominated solutions found during the evolutionary process and includes a mechanism to mutate the individuals in their corresponding external population region. As a study case, the structure-control design of a serial-parallel manipulator with its control system is stated as a dynamic optimization problem and is solved by using the proposed approach. A comparative analysis shows that the multi-objective exhaustive exploitation differential evolution obtained a superior performance in the structure-control design framework than a DE algorithm which did not consider the proposal. Hence, the resulting designs provide better trade-offs between the structure-control performance functions.     

A Global Optimality Principle for Fully Coupled Mean-field Control Systems

This paper concerns a global optimality principle for fully coupled mean-field control systems.Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^ε that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The com...     

Trajectory Planning and Feedforward Control Design for the Temperature Distribution in a Cuboid

The design of a feedforward tracking controller is considered for the temperature distribution in a cuboid, where the temperature on a single lateral surface can be arbitrarily prescribed by a control input. It is shown that there exists a so–called flat or basic output, which allows to explicitly derive the inverse infinite–dimensional system representation suitable for trajectory planning and for the determination of the respective control input necessary to track the desired trajectory in open–loop. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Feedforward Control for a Non-Uniform Euler-Bernoulli Beam

Flatness-based motion planning is considered for an Euler-Bernoulli beam with viscous damping by introducing a systematic spectral approach, which is based on the Riesz spectral properties of the system operator. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Necessary Optimality Conditions for Singular Controls in Dynamical Systems with a Delay in Control

Abstract

In this article, an optimal control problem with a delay in control is considered. The second-order necessary condition is obtained for the optimality of singular (in the sense of the maximum principle) control. Also, the notion of degenerate singular control of order k (k?≥?1) is introduced and for optimality of this, the high-order necessary condition is obtained. Moreover, while studying the problem, one of the strengthened version of an analog of the maximum principle is shown. Finally, the rich content of the obtained results is illustrated by specific examples.     

Feasible Perturbations of Control Systems with Pure State Constraints and Applications to Second-Order Optimality Conditions

We propose second-order necessary optimality conditions for optimal control problems with very general state and control constraints which hold true under weak regularity assumptions on the data. In particular the pure state constraints are general closed sets, the optimal control is supposed to be merely measurable and the dynamics may be discontinuous in the time variable as well. These results are obtained by an approach based on local perturbations of the reference process by second-order tangent directions. This method allows direct and quite simple proofs.     

Optimality Conditions for Nonregular Optimal Control Problems and Duality

We define a new class of optimal control problems and show that this class is the largest one of control problems where every admissible process that satisfies the Extended Pontryaguin Maximum Principle is an optimal solution of nonregular optimal control problems. In this class of problems the local and global minimum coincide. A dual problem is also proposed, which may be seen as a generalization of the Mond–Weir-type dual problem, and it is shown that the 2-invexity notion is a necessary and su?cient condition to establish weak, strong, and converse duality results between a nonregular optimal control problem and its dual problem. We also present an example to illustrate our results.     

Mechatronic Design of the 2 DOF PRRRP Parallel Robot

Mechatronics consists in integration of three fields in engineering: mechanics, electronics and information technology. The paradigm of mechatronics is the integration concept, being the first step in the design of complex mechatronic systems. The need for an integrated approach to the design of complex engineering system involving electronic engineering, mechanical engineering and computing has led to the growth of the concept of mechatronics. The paper presents details regarding the integration process for the kinematic axis in mechatronic. The example of the positioning system based on dc motor and screw–nut transmission is analysed. This actuator is further used for driving a 2 DOF PRRRP parallel robot. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hierarchical Adaptive Techniques for Optimizing Control of Large-Scale Steady-State Systems: Optimality, Iterative Strategies,and their Convergence

A hierarchical structure for on-line steady-state optimizingcontrol of interconnected systems is discussed which utilizesthe available mathematical model more efficiently than in previoustechniques, in spite of large model-reality differences. Thestructure is of an iterative type and uses both the mathematicalmodel of the system and the system output measurements. Thestructure produces a control which satisfies necessary optimalityconditions, provided that the system mathematical model is point-parametric.Several iterative strategies for finding a solution are presented.The strategies are compared with respect to their applicability,the total number of set-point changes needed to find solution,and the amount of information exchanged between control unitsand process during iterations.     

Weak and Strong Optimality Conditions for Constrained Control Problems with Discontinuous Control

In recent years, sufficient optimality criteria and solution stability in optimal control have been investigated widely and used in the analysis of discrete numerical methods. These results were concerned mainly with weak local optima, whereas strong optimality has been considered often as a purely theoretical aspect. In this paper, we show via an example problem how weak the weak local optimality can be and derive new strong optimality conditions. The criteria are suitable for practical verification and can be applied to the case of discontinuous controls with changes in the set of active constraints.     

Optimality Conditions for State-Constrained Dirichlet Boundary Control Problems

In this paper, we prove that the combination of representation theorems for additive measures introduced in Ref. 1, together with a Lagrange multiplier theorem, leads to a short and direct proof of the optimality conditions for Dirichlet control problems with pointwise state constraints.     

On Optimality of the FCFS Discipline in Multiserver Queueing Systems and Networks

Siberian Mathematical Journal -     

An Approach to the Design of Nonlinear Control Systems

A method is proposed for the design of nonlinear systems with an additive control input. The method is based on the Alekseev integral equation and a design procedure developed by the present author, which has been used previously for nonlinear, time-dependent endpoint systems.     

Strong Local Optimality Conditions for State Constrained Control Problems

In this paper first- and second-order optimality conditions for strong local minimum are presented for optimal control problems with pure state set-inclusion constraints. The first-order condition is of Pontryagin type, while the second-order condition is of the form of an accessory problem associated with the strong local minimality. This latter condition contains an extra term reflecting the presence of the pure state constraints.     

On Global Optimality Conditions for Nonlinear Optimal Control Problems

Let a trajectory and control pair maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g( (T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair on [0,T], and if there is no another pair (x,u) such that g(x(T))=g( (T)), then is a global maximizer.