Bayesian optimization of pump operations in water distribution systems

Bayesian optimization has become a widely used tool in the optimization and machine learning communities. It is suitable to problems as simulation/optimization and/or with an objective function computationally expensive to evaluate. Bayesian optimization is based on a surrogate probabilistic model of the objective whose mean and variance are sequentially updated using the observations and an “acquisition” function based on the model, which sets the next observation at the most “promising” point. The most used surrogate model is the Gaussian Process which is the basis of well-known Kriging algorithms. In this paper, the authors consider the pump scheduling optimization problem in a Water Distribution Network with both ON/OFF and variable speed pumps. In a global optimization model, accounting for time patterns of demand and energy price allows significant cost savings. Nonlinearities, and binary decisions in the case of ON/OFF pumps, make pump scheduling optimization computationally challenging, even for small Water Distribution Networks. The well-known EPANET simulator is used to compute the energy cost associated to a pump schedule and to verify that hydraulic constraints are not violated and demand is met. Two Bayesian Optimization approaches are proposed in this paper, where the surrogate model is based on a Gaussian Process and a Random Forest, respectively. Both approaches are tested with different acquisition functions on a set of test functions, a benchmark Water Distribution Network from the literature and a large-scale real-life Water Distribution Network in Milan, Italy.     

Decomposition technique for minimum time trajectories

A decomposition technique is presented for minimum-time trajectories which are characterized by intermediate constraints and discontinuities. The optimization of such multiple are trajectories is usually a formidable task. One optimization method, trajectory decomposition, breaks the original trajectory at points of discontinuity into separate arcs and then optimizes each are subject to prescribed boundary conditions. This constitutes a first level of control. Each first-level solution is evaluated by a second-level controller, which iteratively specifies new are boundary conditions in order to achieve an optimum solution. Unfortunately, this two-level method cannot be applied directly to minimum-time trajectories. The two-level trajectory decomposition method is extended here to a three-level technique for treating the minimum-time trajectory. The first level again optimizes each are for specified intervention parameters. The new second level, the time interface controller, exploits certain homogeneity properties to satisfy time transversality conditions at all boundaries and to couple the first-level solution arcs in time. The third level, the state interface controller, satisfies state transversality conditions at the arc junctions iteratively while driving the trajectory to its optimum. The new three-level procedure represents a feasible decomposition because each solution trajectory in the iterative sequence is physically realizable. The technique also offers a decentralization of control effort and reduction of initial-value sensitivities. An example problem is formulated.     

Sufficiency for Optimal Control Problems Involving Parameters

The optimal control problem is extended to the case where the performance index, the differential constraints, and the prescribed final conditions contain parameters. The sufficient condition for a minimum is derived for nonsingular problems using the sweep method. As expected, it involves the finiteness of a matrix or the location of the conjugate point. The minimum-time navigation problem is solved as a fixed final time problem to illustrate the application of the theory.     

Exact minimum-time control of a distributed system using a traveling wave formulation

In this paper, the minimum-time control problem for rest-to-rest translation of a one-dimensional second-order distributed parameter system by means of two bounded control inputs at the ends is solved. A traveling wave formulation allows the problem to be solved exactly, i.e., without modal truncation. It is found that the minimum-time control is not bang-bang, as it is for systems with a finite number of degrees of freedom. Rather, it is bang-off-bang, where a period of control inactivity in the middle of the control time interval is required for synchronization with waves propagated through the system.This research was supported in part by AFOSR Grant No. AFOSR-90-0297. The helpful suggestions of the referees are gratefully acknowledged.     

更一般高阶非完整系统的指数调节

研究了一类更具有一般性的强漂移高阶非完整系统的指数调节问题.首先通过指数形式的input-state-scaling不连续变换将原x子系统的指数调节问题转化为变换后z子系统的镇定问题,并有效克服x子系统在控制输入u₀=0时不能控的问题.然后基于"加幂积分器"反推方法设计鲁棒控制器,在新的切换策略下,使闭环系统状态指数收敛到零点.仿真例子验证了所提方法的有效性.     

A simple method of chaos control for a class of chaotic discrete-time systems

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called “odd eigenvalues number limitation” of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.     

Continuous-review inventory problem with random supply interruptions

This paper considers a continuous-review stochastic inventory problem with random demand and random lead-time where supply may be disrupted due to machine breakdowns, strikes or other randomly occurring events. The supplier availability is modelled as a semi-Markov process (more specifically, as an alternating renewal process). The standard (q, r) policy is used when the supplier is available (ON), i.e., when the inventory position reaches the reorder point r, q units are ordered to raise the inventory position to the target level of R = q + r. The form of the policy changes when the supplier becomes unavailable (OFF) in which case orders cannot be placed when the reorder point r is reached. However, as soon as the supplier becomes available again one orders enough to bring the inventory position up to the target level of R. The regenerative cycles are identified by observing the inventory position process. We construct the average cost per time objective function using the renewal reward theorem. It is assumed that the duration of the ON period is E_k (i.e., k-stage Erlangian) and the OFF period is general. In analogy with queuing notation we call this an E_k/G system. By employing the ‘method of stages’, we obtain a problem with a larger state space for the ON/OFF stochastic process; but the resulting ON process can now be analyzed using Markovian techniques. For asymptotic values of q, the objective function assumes a particularly simple form which is shown to be convex under mild restrictions on the density functions of demand. Numerical examples illustrate the results.     

Sliding mode control for chaotic systems based on LMI

This paper investigates the chaos control problem for a general class of chaotic systems. A feedback controller is established to guarantee asymptotical stability of the chaotic systems based on the sliding mode control theory. A new reaching law is introduced to solve the chattering problem that is produced by traditional sliding mode control. A dynamic compensator is designed to improve the performance of the closed-loop system in sliding mode, and its parameter is obtained from a linear matrix inequality (LMI). Simulation results for the well known Chua’s circuit and Lorenz chaotic system are provided to illustrate the effectiveness of the proposed scheme.     

Computational Method for Time-Optimal Switching Control

An efficient algorithm, called the time-optimal switching (TOS) algorithm, is proposed for the time-optimal switching control of nonlinear systems with a single control input. The problem is formulated in the arc times space, arc times being the durations of the arcs. A feasible switching control, or as a special case bang-bang control, is found using the STC method previously developed by the authors to get from an initial point to a target point with a given number of switchings. Then, by means of constrained optimization techniques, the cost being considered as the summation of the arc times, a minimum-time switching control solution is obtained. Example applications of the TOS algorithm involving second-order and third-order systems are presented. Comparisons are made with a well-known general optimal control software package to demonstrate the efficiency of the algorithm.     

Robust reliable stabilization of uncertain switched neutral systems with delayed switching

This paper investigates the problem of robust reliable control for a class of uncertain switched neutral systems under asynchronous switching, where the switching instants of the controller experience delays with respect to those of the system and the parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee exponential stability and reliability for switched neutral systems, and the dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.     

State feedback control of condition/event systems

We consider the problem of synthesizing state feedback control policies for condition/event (C/E) systems where the control signals can be both conditions, which enable and inhibit state transitions, and events, which force state transitions. To represent the causal structure of condition and event feedback, a new feedback composition is defined. An algorithm is presented for synthesizing state feedback policies that keep the state of the C/E system out of a given set of forbidden states. The problem formulation and solution is illustrated for a process control example.     

Control synthesis for discrete time systems with control and state bounds in the presence of disturbances

The problem of control in the presence of unknown but limited disturbance for a discrete-time linear system with polyhedral input and state bounds is investigated. Two problems are considered: that of reaching an assigned target set in the state space; and that of keeping the state in a given region using the available controls. In both cases, a solution is given via linear programming. A computational procedure for the control synthesis is proposed which can be implemented to obtain a feedback control.The author thanks Professor G. Leitmann for his helpful suggestions.     

Self-adaptive congestion control for multiclass intermittent connections in a communication network

A Markovian model for intermittent connections of various classes in a communication network is established and investigated. Any connection alternates between being OFF (idle) or ON (active, with data to transmit), and evolves in a way depending only on its class and the state of the network, in particular for the routes it uses among the network nodes to transmit data. The congestion of a given node is a functional of the throughputs of all ON connections going through it, and causes losses to these connections. Any ON connection reacts to its losses by self-adapting its throughput in TCP-like fashion so as to control network congestion. The connections interact through this feedback loop. The system constituted of their states (either OFF, or ON with some throughput) evolves in Markovian fashion, and since the number of connections in each class is potentially huge, a mean-field limit result with an adequate scaling is proved so as to reduce dimensionality. The limit is a nonlinear Markov process given by a McKean?CVlasov equation, of dimension the number of classes. It is then proved that the stationary distributions of the limit can be expressed in terms of the solutions of a finite-dimensional fixed-point equation.     

Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping

In this paper, an adaptive fuzzy output feedback approach is proposed for a single-link robotic manipulator coupled to a brushed direct current (DC) motor with a nonrigid joint. The controller is designed to compensate for the nonlinear dynamics associated with the mechanical subsystem and the electrical subsystems while only requiring the measurements of link position. Using fuzzy logic systems to approximate the unknown nonlinearities, an adaptive fuzzy filter observer is designed to estimate the immeasurable states. By combining the adaptive backstepping and dynamic surface control (DSC) techniques, an adaptive fuzzy output feedback control approach is developed. Stability proof of the overall closed-loop system is given via the Lyapunov direct method. Three key advantages of our scheme are as follows: (i) the proposed adaptive fuzzy control approach does not require that all the states of the system be measured directly, (ii) the proposed control approach can solve the control problem of robotic manipulators with unknown nonlinear uncertainties, and (iii) the problem of “explosion of complexity” existing in the conventional backstepping control methods is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Design,modelling and simulation of a new nonlinear and full adaptive backstepping speed tracking controller for uncertain PMSM

In this study, a new nonlinear and full adaptive backstepping speed tracking control scheme is developed for an uncertain permanent magnet synchronous motor (PMSM). Except for the number of pole pairs, all the other parameters in both PMSM and load dynamics are assumed unknown. Three phase currents and rotor speed are supposed to be measurable and available for feedback in the controller design. By designing virtual control inputs and choosing appropriate Lyapunov functions, the final control and parameter estimation laws are derived. The overall control system possesses global asymptotic stability; all the signals in the closed loop system remain bounded, according to stability analysis results based on Lyapunov stability theory. Further, the proposed controller does not require computation of regression matrices, with the result that take the nonlinearities in quite general. Simulation results clearly exhibit that the controller guarantees tracking of a time varying desired reference speed trajectory under all the uncertainties in both PMSM and load dynamics without singularity and overparameterization. The results also show that all the parameter estimates converge to their true values on account of the fact that reference speed signal chosen to be sufficiently rich ensures persistency of excitation condition. Consequently, the proposed controller ensures strong robustness against all the parameter uncertainties and unknown bounded load torque disturbance in the PMSM drive system. Numerical simulations demonstrate the performance and feasibility of the proposed controller.     

On the terminal control problem

A minimum-time problem is considered, where the final point is locally controllable. It is shown that it is possible to construct a suboptimal control with a transfer time close to the optimal transfer time of the relaxed system. The resulting trajectory will satisfy initial and final conditions. Furthermore, it is shown that, if an optimal solution exists for the problem, then this optimal solution is also an optimal solution of the relaxed problem. In this case, the relaxed problem need not be solved.The authors wish to thank Dr. D. Hazan, Scientific Department, Ministry of Defense, Israel, for a fruitful discussion of this problem.     

Model predictive control for switched systems with a novel mixed time/event-triggering mechanism

This paper investigates observer-based model predictive control (MPC) for switched systems with a mixed time/event-triggering mechanism. The problem of predictive control that can achieve receding horizon optimization is considered and solved by minimizing an upper bound of the quadratic cost function. Since the system state may not be fully measured in practice, state observers are employed to estimate. A mixed mechanism including adaptive event-triggering and time-triggering is proposed, which can be switched determined by a threshold describing system performance to better balance system resource utilization and performance requirements. Then, a closed-loop switched system subject to networked-time-delay is modeled. Piecewise Lyapunov function technique and average dwell time approach are utilized to ensure asymptotical stability. Afterwards, MPC controller construction problem is turned into a LMIs feasibility problem. A new solving method of sufficient conditions for co-design of the state observers, feedback controllers and mixed triggering mechanism is derived. Lastly, simulation examples illustrate the correctness and advantages of research content.     

Optimal control of continuity equations

An optimal control problem for the continuity equation is considered. The aim of a “controller” is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular case of the problem, where an initial distribution is absolutely continuous with smooth density and the target set has certain regularity properties, a necessary optimality condition is derived. It is shown that for the general problem one may construct a perturbed problem that satisfies all the assumptions of the necessary optimality condition, and any optimal control for the perturbed problem, is nearly optimal for the original one.     

Quantized control for networked switched systems under denial-of-service attacks via a barrier event-triggered mechanism

This paper studies the quantized control problem for networked switched systems (NSSs) under denial-of-service (DoS) attacks. The quantized state information, together with the switching signal, is transmitted to the controller through a network. In order to reduce communication consumption and controller update frequency, a barrier event-triggered mechanism is utilized to monitor the state at discrete time. Because of the event-triggered mechanism and the DoS attacks on the network, the mismatch between the system mode and the controller mode is thus frequently encountered, which may lead to quantization saturation and system instability. To solve the problem, an update rule is presented for the dynamic quantizer by switching between zooming in and zooming out of the zooming variable, and a feedback controller is proposed with a jointly designed event-triggered mechanism and a dynamic quantizer. Sufficient conditions on the constraints of DoS frequency and duration are obtained to ensure the exponential stability of the switched system. The effectiveness of the obtained results is illustrated by simulation examples and comparative studies.     

On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

We consider multiplexers in discrete time fed by the superposition of Ternary Markov Sources. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.