Nash-optimization distributed model predictive control for multi mobile robots formation

This paper investigates the distributed model predictive control (DMPC) problem for multi mobile robots. The distributed system model is obtained by the kinematic model of single mobile robot. By including the coupling terms in the cost function, cooperation between subsystems can be incorporated in the distributed control problem. Then, each robot has its own optimal control problem, and neighboring subsystems can exchange information with one another by using wireless communication. The distributed model predictive control problem is formulated by the local cost function and solved by using Nash-optimization algorithm. The convergence condition of the proposed algorithm is presented. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.     

An approximation to optimal modal control

An approximation to the optimal modal control in terms of the first, lowest, mode of the distributed system is proposed. It is assumed that the modes occur with different probabilities and the expected value of the usual cost functional is minimized. The piecewise modal approximation as introduced in this paper is optimal for the lowest mode, and approximately optimal for other modes. The overall expected value is still close to the optimal due to the heavy weight put on the lowest mode. Simulation results on a perfectly conducting string stressed by an electric field are presented.     

An optimal control problem for a class of distributed parameter systems

The optimal control of a class of linear deterministic time-invariant multi-dimensional distributed systems is considered. The unconstrained optimal control problem is formulated as a quadratic minimisation in a real Hilbert space. A conjugate gradient minimisation technique is employed in its solution. The effect of constraints on the control variables is included by adding penalty terms to the performance criterion. This reduces the constrained optimisation to a series of unconstrained minimisations in Hilbert space. A two-dimensional heat conduction system is then considered as an illustrative example. Values for its Green's function are obtained using a numerical technique.     

Optimal control of thermoelastic beam vibrations by piezoelectric actuation

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a single piezoelectric actuator. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations. Numerical results are presented to demonstrate the effectiveness and the applicability of the proposed method.     

Design and experimental testing of an optimization-based flow control algorithm for Energy Harvesting Wireless Sensor Networks

In this paper a distributed flow control law is proposed to maximize throughput and to minimize energy consumption in Energy Harvesting Wireless Sensor Networks (EH-WSNs). We preliminary recast the control problem in terms of primal–dual optimization one taking into account the bandwidth and energy autonomy node constraint. Then, we devise a distributed flow rate control implemented at each node that allows the overall network to converge to the optimal solution of the original problem. The closed loop EH-WSN stability and convergence to the optimal equilibrium are proven. The effectiveness of the proposed control law in terms of throughput and network lifetime performance is experimentally validated by a small representative EH-WSN. The experimental results are in a good agreement with the theoretical ones.     

分布参数系统边界控制的Haar小波算法

由于分布参数系统通常由偏微分方程描述,采用解析法求解分布参数系统最优边界控制问题,是非常难以解决的.正交函数逼近的方法在分布参数系统控制方面,已经取得了较好的效果.Haar小波作为正交基函数,利用小波的一些运算及变换矩阵,将分布参数系统转化为集总参数系统,再求其逼近解.仿真示例验证了所提出的算法是非常有效的.该方法为分布参数系统的控制算法提出了一条新的解决方案.     

Optimal Signaling Policies for Decentralized Multicontroller Stabilizability Over Communication Channels

In this note, we study the problem of distributed control over communication channels, where a number of distributed stations collaborate to stabilize a linear system. We quantify the rate requirements and obtain optimal signaling, coding and control schemes for decentralized stabilizability in such multicontroller systems. We show that in the absence of a centralized decoder at the plant, there is in general a rate loss in decentralized systems as compared to a centralized system. This result is in contrast with the absence of rate loss in the stabilization of multisensor systems. Furthermore, there is rate loss even if explicit channels are available between the stations. We obtain the minimum data rates needed in terms of the open-loop system matrix and the connectivity graph of the decentralized system, and obtain the optimal signaling policies. We also present constructions leading to stability. In addition, we show that if there are dedicated channels connecting the controllers, rate requirements become more lenient, and as a result strong connectivity is not required for decentralized stabilizability. We determine the minimum number of such external channels leading to a stable system, in case strong connectivity is absent.     

Optimal and suboptimal control policies for a solar collector system

An optimal control problem to maximize the net energy gathered by a flat-plate solar collector system by controlling the collector fluid flow rate is investigated. The problem is formulated in terms of a distributed parameter system and solved using the method of characteristics. It is shown that if the pump of the collector loop is such that its pumping power is greater than a linear function of the fluid velocity, then the optimal control policy is one in which the fluid flow is instantly switched between zero and maximum rates. Necessary conditions that determine the optimal switching times are derived. Because the resultant switching function of the optimal policy is shown to be decomposable into two parts, one that depends on the state of the system and another that requires a priori knowledge of the solar intensity over the entire period of operation, a suboptimal control policy that can be implemented by an on/off feedback controller with hysteresis is proposed. When this suboptimal policy is compared with the optimal policy, it is shown that on a clear day with sufficient solar insolation to dictate a two-switch optimal policy, the two policies are identical. Under other weather conditions, the feedback suboptimal controller will keep the pump off for a slightly shorter period of time than the time dictated by the optimal control.     

Distributed Secondary Control and Optimal Power Sharing in Microgrids

We address the control problem of microgrids and present a fully distributed control system which consists of primary controller, secondary controller, and optimal active power sharing controller. Different from the existing control structure in microgrids, all these controllers are implemented as local controllers at each distributed generator. Thus, the requirement for a central controller is obviated. The performance analysis of the proposed control systems is provided, and the finite-time convergence properties for distributed secondary frequency and voltage controllers are achieved. Moreover, the distributed control system possesses the optimal active power sharing property. In the end, a microgrid test system is investigated to validate the effectiveness of the proposed control strategies.      

System level synthesis

This article surveys the System Level Synthesis framework, which presents a novel perspective on constrained robust and optimal controller synthesis for linear systems. We show how SLS shifts the controller synthesis task from the design of a controller to the design of the entire closed loop system, and highlight the benefits of this approach in terms of scalability and transparency. We emphasize two particular applications of SLS, namely large-scale distributed optimal control and robust control. In the case of distributed control, we show how SLS allows for localized controllers to be computed, extending robust and optimal control methods to large-scale systems under practical and realistic assumptions. In the case of robust control, we show how SLS allows for novel design methodologies that, for the first time, quantify the degradation in performance of a robust controller due to model uncertainty – such transparency is key in allowing robust control methods to interact, in a principled way, with modern techniques from machine learning and statistical inference. Throughout, we emphasize practical and efficient computational solutions, and demonstrate our methods on easy to understand case studies.     

Robust stabilizability of normalized coprime factors: the infinite-dimensional case

The problem of robustly stabilizing a linear system subject to H_∞-bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite-dimensional systems. This class has possible unbounded, finite-rank input and output operators, which include many delay and distributed systems. The optimal stability margin is expressed in terms of the solutions of the control and filter algebraic Riccati equations.     

Stabilization of linear autonomous systems of differential equations with distributed delay

Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that coefficients of the optimal stabilizing control are defined by algebraic and functional-differential Riccati equations. To find solutions to Riccati equations, the method of successive approximations is used. The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization. A class of control laws for which the posed problem admits an analytic solution is described.     

Decentralized optimization for distributed-lag models of discrete systems

The approach discussed in this paper solves a general class of optimization problems for discrete dynamic systems which include distributed lag, distributed and/or multiple pure delays, and constraints both in state and control variables. The overall system equation of this problem is described by a multidimensional nonlinear difference equation of high-order which is called the distributed-lag model. Applying Lagrange duality theory to the original problem, the dual problem is formulated, and the decomposition of the optimization process in stage is obtained. It is shown that by solving the dual problem the delay terms can be easily handled and the optimal solution to the original problem is obtained without reducing the multi-dimensional high-order system equation to a conventional larger dimensional first-order system equation. It is also shown that the dual decentralized method in this paper is easier to cope with state and control constraints than the primal method in the space of control, i.e. gradient and other techniques. The approach developed in this paper is compared with other methods using a simple example, and is applied to a combined marketing and production control problem. Some computational results are included.     

Optimal sequential and distributed fusion for state estimation in cross-correlated noise

This paper is concerned with the optimal state estimation for linear systems when the noises of different sensors are cross-correlated and also coupled with the system noise of the previous step. We derive the optimal linear estimation in a sequential form and for distributed fusion. They are both compared with the optimal batch fusion, suboptimal batch fusion, suboptimal sequential fusion, and the suboptimal distributed fusion where the cross-correlation between the noises are neglected. The comparison is in terms of theoretical filter mean square error and the real root mean square error. Simulation on a target tracking example is given to show the effectiveness of the presented algorithms.     

Optimal control of distributed bilinear systems

The optimal control problem for a bilinear distributed parameter system subject to a quadratic cost functional is solved. It is shown that the optimal control is given by a convergent power series in the state with tensor coefficients.     

Optimal control of linear systems with large and variable input delays

This paper proposes an optimal control law for linear systems affected by input delays. Specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a DDE without distributed terms. The solution can be seen as a chain of predictors whose size depends on the maximum delay.     

Block sparse design of distributed controllers for dynamical network systems

This study proposes a controller design method based on block sparse optimization for dynamical network systems. The objective of the controller is to stabilize dynamical network systems with a given convergence rate. The block sparse optimization minimizes the number of controlled nodes. This study is unique in that the structure of the controller is constrained by the network topology of the system. Additionally, the proposed design problem is separable in terms of the distributed optimization over networks. The proposed method is applicable to controller design for the pinning control of consensus systems and the optimal vaccine allocation for epidemic spreading processes.     

An alternative formulation of a distributed-parameter optimal cotrol problem applied to nuclear shielding

An alternative formalism for optimal control of distributed parameter systems is proposed. Necessary conditions for optimality and transversality conditions are developed for a class of distributed-parameter systems. It is shown that when the distributed system becomes a lumped-parameter one, the results obtained become identical to known results of optimal control of lumped systems. The formalism developed is applied to solve a problem of optimal design of a shielding installation around a neutron source.     

Optimal control of a solar collector loop using a distributed-lumped model

This paper considers the optimal control of a solar collector loop described by a bilinear distributed parameter model for the collector fluid temperature and a bilinear lumped parameter model for the storage fluid temperature. The objective is to control the collector fluid velocity so as to maximize the net energy collected over a fixed time period. Necessary conditions for optimality, given by a set of equations whose solution yields the optimal control, are derived. It is shown that the optimal control is an open-loop, bang-bang control which depends on two terms: a measurable quantity which depends on the state of the collector fluid, and a quantity which depends on a future knowledge of the weather data. It is also shown that for the case in which only two switches occur during the period of operation, the optimal control depends only on the temperature difference across the collector. Thus, one can construct a feedback on/off controller for the system provided that it is known a priori that only two switches will occur during the time interval under consideration.     

Distributed match-making

In many distributed computing environments, processes are concurrently executed by nodes in a store- and-forward communication network. Distributed control issues as diverse as name server, mutual exclusion, and replicated data management involve making matches between such processes. We propose a formal problem called “distributed match-making” as the generic paradigm. Algorithms for distributed match-making are developed and the complexity is investigated in terms of messages and in terms of storage needed. Lower bounds on the complexity of distributed match-making are established. Optimal algorithms, or nearly optimal algorithms, are given for particular network topologies.