Event-triggered near optimal adaptive control of interconnected systems

Increased interest in complex interconnected systems like smart-grid, cyber manufacturing have attracted researchers to develop optimal adaptive control schemes to elicit a desired performance when the complex system dynamics are uncertain. In this dissertation, motivated by the fact that aperiodic event sampling saves network resources while ensuring system stability, a suite of novel event-sampled distributed near-optimal adaptive control schemes are introduced for uncertain linear and affine nonlinear interconnected systems in a forward-in-time and online manner. First, a novel stochastic hybrid Q-learning scheme is proposed to generate optimal adaptive control law and to accelerate the learning process in the presence of random delays and packet losses resulting from the communication network for an uncertain linear interconnected system. Subsequently, a novel online reinforcement learning (RL) approach is proposed to solve the Hamilton-Jacobi-Bellman (HJB) equation by using neural networks (NNs) for generating distributed optimal control of nonlinear interconnected systems using state and output feedback. To relax the state vector measurements, distributed observers are introduced. Next, using RL, an improved NN learning rule is derived to solve the HJB equation for uncertain nonlinear interconnected systems with event-triggered feedback. Distributed NN identifiers are introduced both for approximating the uncertain nonlinear dynamics and to serve as a model for online exploration. Next, the control policy and the event-sampling errors are considered as non-cooperative players and a min-max optimization problem is formulated for linear and affine nonlinear systems by using zero-sum game approach for simultaneous optimization of both the control policy and the event based sampling instants. The net result is the development of optimal adaptive event-triggered control of uncertain dynamic systems --Abstract, page iv

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems

Plug-and-Play Model Predictive Control based on robust control invariant sets

In this paper we consider a linear system represented by a coupling graph between subsystems and propose a distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Most importantly, as in Riverso et al., 2012 our design procedure enables plug-and-play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the design of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method hinges on local tube MPC controllers based on robust control invariant sets and it advances the PnP design procedure proposed in Riverso et al., 2012 in several directions. Quite notably, using recent results in the computation of robust control invariant sets, we show how critical steps in the design of a local controller can be solved through linear programming. Finally, an application of the proposed control design procedure to frequency control in power networks is presented

Formal methods for resilient control

Many systems operate in uncertain, possibly adversarial environments, and their successful operation is contingent upon satisfying specific requirements, optimal performance, and ability to recover from unexpected situations. Examples are prevalent in many engineering disciplines such as transportation, robotics, energy, and biological systems. This thesis studies designing correct, resilient, and optimal controllers for discrete-time complex systems from elaborate, possibly vague, specifications. The first part of the contributions of this thesis is a framework for optimal control of non-deterministic hybrid systems from specifications described by signal temporal logic (STL), which can express a broad spectrum of interesting properties. The method is optimization-based and has several advantages over the existing techniques. When satisfying the specification is impossible, the degree of violation - characterized by STL quantitative semantics - is minimized. The computational limitations are discussed. The focus of second part is on specific types of systems and specifications for which controllers are synthesized efficiently. A class of monotone systems is introduced for which formal synthesis is scalable and almost complete. It is shown that hybrid macroscopic traffic models fall into this class. Novel techniques in modular verification and synthesis are employed for distributed optimal control, and their usefulness is shown for large-scale traffic management. Apart from monotone systems, a method is introduced for robust constrained control of networked linear systems with communication constraints. Case studies on longitudinal control of vehicular platoons are presented. The third part is about learning-based control with formal guarantees. Two approaches are studied. First, a formal perspective on adaptive control is provided in which the model is represented by a parametric transition system, and the specification is captured by an automaton. A correct-by-construction framework is developed such that the controller infers the actual parameters and plans accordingly for all possible future transitions and inferences. The second approach is based on hybrid model identification using input-output data. By assuming some limited knowledge of the range of system behaviors, theoretical performance guarantees are provided on implementing the controller designed for the identified model on the original unknown system

Manufacturing systems considered as time domain control systems : receding horizon control and observers

This thesis considers manufacturing systems and model-based controller design, as well as their combinations. The objective of a manufacturing system is to create products from a selected group of raw materials and semifinished goods. In the field of manufacturing systems control is an important issue appearing at various operation levels. At the level of fabrication, for example, control is necessary in order to assure properly working production processes such that products are being fabricated in the desired way. At a higher level in the hierarchy of manufacturing system control, the product streams through the system are controlled in order to satisfy, for example, customer demands in an optimal way. Here, the definition of optimal can be interpreted in various ways, such as "with the least possible costs in terms of money" or "in the shortest possible time". In this research, the attention is focussed on this higher hierarchy level of manufacturing system control. In the literature, many heuristic methods have been developed for the control of a manufacturing system. Nowadays, some heuristicmethods are still being used in combination with operator experience for management of resources and planning of production. However, as the complexity of the manufacturing systems increases rapidly, the (simple) heuristic methods and operator experience will at some point become incapable of finding an optimal control strategy. In this dissertation the potential of consideringmanufacturing system control from a control systems point of view is investigated. The ultimate goal of the research is to eventually obtain a more constructive way to address controller design for manufacturing systems. One control strategy from control systems theory, on which is in particularly focused in this research, is a model-based receding horizon control strategy, known in literature as Model Predictive Control (MPC). Since in manufacturing systems a lot of physical system constraints are involved, like for example finite machine process capacities, finite product storage capacities, finite product arrival rates, etc., the capability for a manufacturing control strategy to handle those constraints is a necessity. One of the key features of model predictive control is the capability of handling constraints in the controller design. This is one of the major motivations to investigate the model predictive control principle as a control strategy for manufacturing systems. Other issues that are important and that the model predictive control design methodology can handle is to enforce optimality, to introduce feedback, and the capability of allowing for mixed continuous and discrete model structures. The later are typically encountered when models of manufacturing systems are derived. The main results that are obtained in this dissertation and that are relevant in the context of manufacturing systems control, but are certainly also relevant beyond this field are: • One has developed an robust computationally friendly nonlinear model predictive control algorithm that can handle model structures with mixed continuous and discrete dynamics. The algorithm can be designed for additive disturbance rejection purposes; • Robustness (with respect to measurement noise) results that are in particulary of interest in the field of nonlinear model predictive control are obtained; • An asymptotically stabilizing output based nonlinear model predictive control scheme for a class of nonlinear discrete-time systems is developed. Results that are relevant in the context of manufacturing systems control are: • It is illustrated howthe aforementioned developed robust computationally friendly nonlinear model predictive control algorithm can be employed to solve a large scale manufacturing control problem in an efficient decentralized manner; • The relation between the so-called event domain modeling approaches for a class of discrete-eventmanufacturing systems to time domainmodels is derived. This results enables one to solve seemingly untractable time domain formulated optimal control problems for a class of manufacturing systems in a tractable manner; • An observer theory for a class of discrete-event manufacturing systems is developed

Correct-By-Construction Control Synthesis for Systems with Disturbance and Uncertainty

This dissertation focuses on correct-by-construction control synthesis for Cyber-Physical Systems (CPS) under model uncertainty and disturbance. CPSs are systems that interact with the physical world and perform complicated dynamic tasks where safety is often the overriding factor. Correct-by-construction control synthesis is a concept that provides formal performance guarantees to closed-loop systems by rigorous mathematic reasoning. Since CPSs interact with the environment, disturbance and modeling uncertainty are critical to the success of the control synthesis. Disturbance and uncertainty may come from a variety of sources, such as exogenous disturbance, the disturbance caused by co-existing controllers and modeling uncertainty. To better accommodate the different types of disturbance and uncertainty, the verification and control synthesis methods must be chosen accordingly. Four approaches are included in this dissertation. First, to deal with exogenous disturbance, a polar algorithm is developed to compute an avoidable set for obstacle avoidance. Second, a supervised learning based method is proposed to design a good student controller that has safety built-in and rarely triggers the intervention of the supervisory controller, thus targeting the design of the student controller. Third, to deal with the disturbance caused by co-existing controllers, a Lyapunov verification method is proposed to formally verify the safety of coexisting controllers while respecting the confidentiality requirement. Finally, a data-driven approach is proposed to deal with model uncertainty. A minimal robust control invariant set is computed for an uncertain dynamic system without a given model by first identifying the set of admissible models and then simultaneously computing the invariant set while selecting the optimal model. The proposed methods are applicable to many real-world applications and reflect the notion of using the structure of the system to achieve performance guarantees without being overly conservative.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145933/1/chenyx_1.pd

Price-based optimal control of electrical power systems

During the past decade, electrical power systems have been going through some major restructuring processes. From monopolistic, highly regulated and one utility controlled operation, a system is being restructured to include many parties competing for energy production and consumption, and for provision of many of the ancillary services necessary for system operation. With the emergence of competitive markets as central operational mechanisms, the prime operational objective has shifted from a centralized, utility cost minimization objective to decentralized, profit maximization objectives of competing parties. The market-based (price-based) operation is shown to be practically the only approach that is capable to simultaneously provide incentives to hold the prices at marginal costs and to minimize the costs. As a result, such an operational structure inherently tends to maximize the social welfare of the system during its operation, and to accelerate developments and applications of new technologies. Another major change that is taking place in today’s power systems is an increasing integration of small-scale distributed generation (DG) units. Since in future power systems, a large amounts of DG will be based on renewable, intermittent energy sources, e.g. wind and sun, these systems will be characterized by significantly larger uncertainties than those of the present power systems. Power markets significantly deviate from standard economics since the demand side is largely disconnected from the market, i.e. it is not price responsive, and it exhibits uncertain, stochastic behavior. Furthermore, since electrical energy cannot be efficiently stored in large quantities, production has to meet these rapidly changing demands in real-time. In future power systems, efficient real-time power balancing schemes will become crucial and even more challenging due to the significant increase of uncertainties by large-scale integration of renewable sources. Physical and security limits on the maximal power flows in the lines of power transmission networks represent crucial system constraints, which must be satisfied to protect the integrity of the system. Creating an efficient congestion management scheme for dealing with these constraints is one of the toughest problems in the electricity market design, as the line power flows are characterized by complex dependencies on nodal power injections. Efficient congestion control has to account for those limits by adequately transforming them into market signals, i.e. into electricity prices. One of the main contributions of this thesis is the development of a novel dynamic, distributed feedback control scheme for optimal real-time update of electricity prices. The developed controller (which is called the KKT controller in the thesis) reacts on the network frequency deviation as a measure of power imbalance in the system and on measured violations of line flow limits in a transmission network. The output of the controller is a vector of nodal prices. Each producer/consumer in the system is allowed to autonomously react on the announced price by adjusting its production/consumption level to maximize its own benefit. Under the hypothesis of global asymptotic stability of the closed-loop system, the developed control scheme is proven to continuously balance the system by driving it towards the equilibrium where the transmission power flow constraints are satisfied, and where the total social welfare of the system is maximized. One of the advantageous features of the developed control scheme is that, to achieve this goal, it requires no knowledge of marginal cost/benefit functions of producers/consumers in the system (neither is it based on the estimates of those functions). The only system parameters that are explicitly included in the control law are the transmission network parameters, i.e. network topology and line impedances. Furthermore, the developed control law can be implemented in a distributed fashion. More precisely, it can be implemented through a set of nodal controllers, where one nodal controller (NC) is assigned to each node in the network. Each NC acts only on locally available information, i.e. on the measurements from the corresponding node and on the information obtained from NC’s of the adjacent nodes. The communication network graph among NC’s is therefore the same as the graph of the underlying physical network. Any change is the network topology requires only simple adjustments in NC’s that are local to the location of the change. To impose the hard constraints on the level to which the transmission network lines are overloaded during the transient periods following relatively large power imbalances in the system, a novel price-based hybrid model predictive control (MPC) scheme has been developed. The MPC control action adds corrective signals to the output of the KKT controller, i.e. to the nodal prices, and acts only when the predictions indicate that the imposed hard constraint will be violated. In any other case, output of the MPC controller is zero and only the KKT controller is active. Under certain hypothesis, recursive feasibility and asymptotic stability of the closed-loop system with the hybrid MPC controller are proven. Next contribution of this thesis is formulation of the autonomous power networks concept as a multilayered operational structure of future power systems, which allows for efficient large-scale integration of DG and smallscale consumers into power and ancillary service markets, i.e. markets for different classes of reserve capacities. An autonomous power network (AN) is an aggregation of networked producers and consumers, whose operation is coordinated/controlled with one central unit (AN market agent). By performing optimal dispatching and unit commitment services, the main goals of an AN market agent is to efficiently deploy the AN’s internal resources by its active involvement in power and ancillary service markets, and to optimally account for the local reliability needs. An autonomous power network is further defined as a major building block of power system operation, which is capable of keeping track of its contribution to the uncertainty in the overall system, and is capable of bearing the responsibility for it. With the introduction of such entities, the conditions are created that allow for the emergence of novel, competitive ancillary service market structures. More precisely, in ANs based power systems, each AN can be both producer and consumer of ancillary services, and ancillary service markets are characterized by double-sided competition, what is in contrast to today’s single-sided ancillary service markets. One of the main implications of this novel operational structure in that, by facilitating competition, it creates the strong incentive for ANs to reduce the uncertainties and to increase reliability of the system. On a more technical side, the AN concept is seen as decentralization and modularization approach for dealing with the future, large scale, complex power systems. As additional contribution of this thesis, motivated by the KKT controller for price-based real-time power balancing and congestion management, the general KKT control paradigm is presented in some detail. The developed control design procedure presents a solution to the problem of regulating a general linear time-invariant dynamical system to a time-varying economically optimal operating point. The system is characterized with a set of exogenous inputs as an abstraction of time-varying loads and disturbances. Economic optimality is defined through a constrained convex optimization problem with a set of system states as decision variables, and with the values of exogenous inputs as parameters in the optimization problem. A KKT controller belongs to a class of dynamic complementarity systems, which has been recently introduced and which has, due to its wide applicability and specific structural properties, gained a significant attention in systems and control community. The results of this thesis add to the list of applications of complementarity systems in control

Design of of model-based controllers via parametric programming

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