Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Switched Stackelberg game analysis of false data injection attacks on networked control systems

summary:This paper is concerned with a security problem for a discrete-time linear networked control system of switched dynamics. The control sequence generated by a remotely located controller is transmitted over a vulnerable communication network, where the control input may be corrupted by false data injection attacks launched by a malicious adversary. Two partially conflicted cost functions are constructed as the quantitative guidelines for both the controller and the attacker, after which a switched Stackelberg game framework is proposed to analyze the interdependent decision-making processes. A receding-horizon switched Stackelberg strategy for the controller is derived subsequently, which, together with the corresponding best response of the attacker, constitutes the switched Stackelberg equilibrium. Furthermore, the asymptotic stability of the closed-loop system under the switched Stackelberg equilibrium is guaranteed if the switching signal exhibits a certain average dwell time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method in this paper

Optimal sensor/actuator placement and switching schemes for control of flexible structures

The vibration control problem for flexible structures is examined within the context of overall controller performance and power reduction. First, the issue of optimal sensor and actuator placement is considered along with its associated control robustness aspects. Then the option of alternately activating subsets of the available devices is investigated. Such option is considered in order to better address the effects of spatiotemporally varying disturbances acting on a flexible structure while reducing the overall energy consumption. Towards the solution to the problem of optimal device placement, three different approaches are proposed. First, a computationally efficient scheme for the simultaneous placement of multiple devices is presented. The second approach proposes a strategy for the optimal placement of sensors and collocated sensor/actuator pairs, taking into account the influence of the spatial distribution of disturbances. The third approach provides a solution to the actuator location problem by incorporating considerations with respect to preferred spatial regions within the flexible structure. Then the second problem named above is considered. Activating a subset of the available and optimally placed actuators and sensors in a flexible structure provides enhanced performance with reduced energy consumption. Such approach of switching on and off different actuating devices, depending on their local-in-time authority, results in a hybrid system. Therefore the proposed work draws on existing results on hybrid systems and includes an additional degree of freedom, whereby both the actuating devices and the control signals allocated to them are switched in and out. To enable this switching an activation strategy, which insures also that stability-under-switching is guaranteed, is required. Three different strategies are considered for such actuators allocation: first a cost-to-go index is considered, then a cost function based on the mechanical energy of the flexible structure and finally a performance index based on the maximum deviation of the transverse displacement. A flexible aluminum plate was chosen to validate and test the proposed approaches. The set up utilized four pairs of collocated piezoceramic patches that serve to provide sensing and actuating capabilities. Extensive numerical simulations were performed for both the placement strategies and the switching policies proposed, in order to predict the behavior of the flexible plate and provide the optimal actuator and sensor locations that were to be affixed on the flexible structure. Finally, to complete the validation process a sequence of experimental tests were performed. The objective of these tests was to compare the performance of the proposed hybrid control system to traditional non switched control schemes. In order to provide a repeatable perturbation, four of the piezoceramic patches were allocated to simulate a spatiotemporally varying disturbance, while the remaining four patches were used as sensors and controlling actuators. The experimental results showed a significant performance improvement for the switched controller over the traditional controller. Moreover the switched controller exhibited improved robustness towards spatiotemporally varying disturbances while the traditional controller showed a significant loss of controller performance. The improvement achieved in vibration control problems could be extended to a wider range of applications. In particular, although this study was concentrated on a rectangular thin plate, the proposed strategies can be applied to emph{any} structure and more generally to any plant whose dynamics can be represented by a second order linear system. For example, by removing the restriction of spatially fixed actuators and sensors, the proposed theory can be applied to the problem of unmanned vehicles control

Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks

A MIMO Multi-hop Control Network (MCN) consists of a MIMO LTI system where the communication between sensors, actuators and computational units is supported by a (wireless) multi-hop communication network, and data flow is performed using scheduling and routing of sensing and actuation data. We provide necessary and sufficient conditions on the plant dynamics and on the communication protocol configuration such that the Fault Detection and Isolation (FDI) problem of failures and malicious attacks to communication nodes can be solved.Comment: 6 page

Foundations of Infrastructure CPS

Infrastructures have been around as long as urban centers, supporting a society’s needs for its planning, operation, and safety. As we move deeper into the 21st century, these infrastructures are becoming smart – they monitor themselves, communicate, and most importantly self-govern, which we denote as Infrastructure CPS. Cyber-physical systems are now becoming increasingly prevalent and possibly even mainstream. With the basics of CPS in place, such as stability, robustness, and reliability properties at a systems level, and hybrid, switched, and eventtriggered properties at a network level, we believe that the time is right to go to the next step, Infrastructure CPS, which forms the focus of the proposed tutorial. We discuss three different foundations, (i) Human Empowerment, (ii) Transactive Control, and (iii) Resilience. This will be followed by two examples, one on the nexus between power and communication infrastructure, and the other between natural gas and electricity, both of which have been investigated extensively of late, and are emerging to be apt illustrations of Infrastructure CPS

State elimination for mixed-integer optimal control of partial differential equations by semigroup theory

Mixed-integer optimal control problems governed by partial differential equations (MIPDECOs) are powerful modeling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by partial differential equations that have the structure of an abstract ordinary differential equation in function space. This allows us to avoid repeated calculations of the states for all time steps, and our approach is applied only once before starting the optimization. The presentation of theoretical results is complemented by numerical experiments

Modelling for robust feedback control of fluid flows

This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an H∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller