A virtual actuator approach for the secure control of networked LPV systems under pulse-width modulated DoS attacks

In this paper, we formulate and analyze the problem of secure control in the context of networked linear parameter varying (LPV) systems. We consider an energy-constrained, pulse-width modulated (PWM) jammer, which corrupts the control communication channel by performing a denial-of-service (DoS) attack. In particular, the malicious attacker is able to erase the data sent to one or more actuators. In order to achieve secure control, we propose a virtual actuator technique under the assumption that the behavior of the attacker has been identified. The main advantage brought by this technique is that the existing components in the control system can be maintained without need of retuning them, since the virtual actuator will perform a reconfiguration of the plant, hiding the attack from the controller point of view. Using Lyapunov-based results that take into account the possible behavior of the attacker, design conditions for calculating the virtual actuators gains are obtained. A numerical example is used to illustrate the proposed secure control strategy.Peer ReviewedPostprint (author's final draft

Switched Kinematic and Force Control for Lower-Limb Motorized Exoskeletons and Functional Electrical Stimulation

Millions of people experience movement deficits from neurological conditions (NCs) that impair their walking ability and leg function. Exercise-based rehabilitation procedures have shown the potential to facilitate neurological reorganization and functional recovery. Lower-limb powered exoskeletons and motorized ergometers have been combined with functional electrical stimulation (FES) to provide repetitive movement, partially reduce the burden of therapists, improve range of motion, and induce therapeutic benefits. FES evokes artificial muscles contractions and can improve muscle mass and strength, and bone density in people with NCs. Stationary cycling is recommended for individuals who cannot perform load-bearing activities or have increased risks of falling. Cycling has been demonstrated to impart physiological and cardiovascular benefits. Motorized FES-cycling combines an electric motor and electrical stimulation of lower-limb muscles to facilitate coordinated, long-duration exercise, while mitigating the inherent muscle fatigue due to FES. Lower-limb exoskeletons coupled with FES, also called neuroprostheses or hybrid exoskeletons, can facilitate continuous, repetitive motion to improve gait function and build muscle capacity. The human-robot interaction during rehabilitative cycling and walking yield a mix of discrete effects (i.e., foot impact, input switching to engage lower-limb muscles and electric motors, etc.) and continuous nonlinear, uncertain, time-varying dynamics. Switching control is necessary to allocate the control inputs to lower-limb muscle groups and electric motors involved during assisted cycling and walking. Kinematic tracking has been the primary control objective for devices that combine FES and electric motors. However, there are force interactions between the machine and the human during cycling and walking that motivate the design of torque-based controllers (i.e., exploit torque or force feedback) to shape the leg dynamics through controlling joint kinematics and kinetics. Technical challenges exist to develop closed-loop feedback control strategies that integrate kinematic and force feedback in the presence of switching and discontinuous effects. The motivation in this dissertation is to design, analyze and implement switching controllers for assisted cycling and walking leveraging kinematic and force feedback while guaranteeing the stability of the human-robot closed-loop system. In Chapter 1, the motivation to design closed-loop controllers for motorized FES-cycling and powered exoskeletons is described. A survey of closed-loop kinematic and force feedback control methods is also introduced related to the tracking objectives presented in the subsequent chapters of the dissertation. In Chapter 2, the dynamics models for walking and assisted cycling are described. First, a bipedal walking system model with switched dynamics is introduced to control a powered lower-limb exoskeleton. Then, a stationary FES-cycling model with nonlinear dynamics and switched control inputs is introduced based on published literature. The muscle stimulation pattern is defined based on the kinematic effectiveness of the rider, which depends on the crank angle. The experimental setup for lower-limb exoskeleton and FES-cycling are described. In Chapter 3, a hierarchical control strategy is developed to interface a cable-driven lower-limb exoskeleton. A two-layer control system is developed to adjust cable tensions and apply torque about the knee joint using a pair of electric motors that provide knee flexion and extension. The control design is segregated into a joint-level control loop and a low-level loop using feedback of the angular positions of the electric motors to mitigate cable slacking. A Lyapunov-based stability analysis is developed to ensure exponential tracking for both control objectives. Moreover, an average dwell time analysis computes an upper bound on the number of motor switches to preserve exponential tracking. Preliminary experimental results in an able-bodied individual are depicted. The developed control strategy is extended and applied to the control of both knee and hip joints in Chapter 4 for treadmill walking. In Chapter 4, a cable-driven lower-limb exoskeleton is integrated with FES for treadmill walking at a constant speed. A nonlinear robust controller is used to activate the quadriceps and hamstrings muscle groups via FES to achieve kinematic tracking about the knee joint. Moreover, electric motors adjust the knee joint stiffness throughout the gait cycle using an integral torque feedback controller. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the kinematic and torque closed-loop error systems, while guaranteeing that the control input signals remain bounded. The developed controllers were tested in real-time walking experiments on a treadmill in three able-bodied individuals at two gait speeds. The experimental results demonstrate the feasibility of coupling a cable-driven exoskeleton with FES for treadmill walking using a switching-based control strategy and exploiting both kinematic and force feedback. In Chapter 5, input-output data is exploited using a finite-time algorithm to estimate the target desired torque leveraging an estimate of the active torque produced by muscles via FES. The convergence rate of the finite-time algorithm can be adjusted by tuning selectable parameters. To achieve cadence and torque tracking for FES-cycling, nonlinear robust tracking controllers are designed for muscles and motor. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the closed-loop cadence error system and global uniformly ultimate bounded (GUUB) torque tracking. A discrete-time Lyapunov-based stability analysis leveraging a recent tool for finite-time systems is developed to ensure convergence and guarantee that the finite-time algorithm is Holder continuous. The developed tracking controllers for the muscles and electric motor and finite-time algorithm to compute the desired torque are implemented in real-time during cycling experiments in seven able-bodied individuals. Multiple cycling trials are implemented with different gain parameters of the finite-time torque algorithm to compare tracking performance for all participants. Chapter 6 highlights the contributions of the developed control methods and provides recommendations for future research extensions

Robust adaptive control of switched systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 141-149).In this thesis, robust adaptive controllers are developed for classes of switched nonlinear systems. Switched systems are those governed by differential equations, which undergo vector field switching due to sudden changes in model characteristics. Such systems arise in many applications such as mechanical systems with contacts, electrical systems with switches, and thermal-fluidic systems with valves and phase changes. The presented controllers guarantee system stability, under typical adaptive control assumptions, for systems with piecewise differentiable bounded parameters and piecewise continuous disturbances without requiring a priori knowledge on such parameters or disturbances. The effect of plant variation and switching is reduced to piecewise continuous and impulsive inputs acting on a Bounded Input Bounded State (BIBS) stable closed loop system. This, in turn, provides a separation between the robust stability and robust performance control problems. The developed methodology provides clear guidelines for steady-state and transient performance optimization and allows for parameter scheduling and multiple model controller adjustment techniques to be utilized with no stability concerns. The results are illustrated for various systems including contact-based robotic manipulation and Atomic Force Microscope (AFM) based nano-manipulation.by Khalid El Rifai.Ph.D

Model predictive control for linear systems: adaptive, distributed and switching implementations

Thanks to substantial past and recent developments, model predictive control has become one of the most relevant advanced control techniques. Nevertheless, many challenges associated to the reliance of MPC on a mathematical model that accurately depicts the controlled process still exist. This thesis is concerned with three of these challenges, placing the focus on constructing mathematically sound MPC controllers that are comparable in complexity to standard MPC implementations. The first part of this thesis tackles the challenge of model uncertainty in time-varying plants. A new dual MPC controller is devised to robustly control the system in presence of parametric uncertainty and simultaneously identify more accurate representations of the plant while in operation. The main feature of the proposed dual controller is the partition of the input, in order to decouple both objectives. Standard robust MPC concepts are combined with a persistence of excitation approach that guarantees the closed-loop data is informative enough to provide accurate estimates. Finally, the adequacy of the estimates for updating the MPC's prediction model is discussed. The second part of this thesis tackles a specific type of time-varying plant usually referred to as switching systems. A new approach to the computation of dwell-times that guarantee admissible and stable switching between mode-specific MPC controllers is proposed. The approach is computationally tractable, even for large scale systems, and relies on the well-known exponential stability result available for standard MPC controllers. The last part of this thesis tackles the challenge of MPC for large-scale networks composed by several subsystems that experience dynamical coupling. In particular, the approach devised in this thesis is non-cooperative, and does not rely on arbitrarily chosen parameters, or centralized initializations. The result is a distributed control algorithm that requires one step of communication between neighbouring subsystems at each sampling time, in order to properly account for the interaction, and provide admissible and stabilizing control

Multi-agent persistent monitoring of a finite set of targets

The general problem of multi-agent persistent monitoring finds applications in a variety of domains ranging from meter to kilometer-scale systems, such as surveillance or environmental monitoring, down to nano-scale systems such as tracking biological macromolecules for studying basic biology and disease. The problem can be cast as moving the agents between targets, acquiring information from or in some fashion controlling the states of the targets. Under this formulation, at least two questions need to be addressed. The first is the design of motion trajectories for the agents as they move among the spatially distributed targets and jointly optimize a given cost function that describes some desired application. The second is the design of the controller that an agent will use at a target to steer the target's state as desired. The first question can be viewed in at least two ways: first, as an optimal control problem with the domain of the targets described as a continuous space, and second as a discrete scheduling task. In this work we focus on the second approach, which formulates the target dynamics as a hybrid automaton, and the geometry of the targets as a graph. We show how to find solutions by translating the scheduling problem into a search for the optimal route. With a route specifying the visiting sequence in place, we derive the optimal time the agent spends at each target analytically. The second question, namely that of steering the target's state, can be formulated from the perspective of the target, rather than the agent. The mobile nature of the agents leads to intermittencontrol, such that the controller is assumed to be disconnected when no agent is at the target. The design of the visiting schedule of agents to one target can affect the reachability (controllability) of this target's control system and the design of any specific controller. Existing test techniques for reachability are combined with the idea of lifting to provide conditions on systems such that reachability is maintained in the presence of periodic disconnections from the controller. While considering an intermittently connected control with constraints on the control authority and in the presence of a disturbance, the concept of 'degree of controllability' is introduced. The degree is measured by a region of states that can be brought back to the origin in a given finite time. The size of this region is estimated to evaluate the performance of a given sequence

Novel characterizations for switched nonlinear systems with average dwell time: further findings

It is well known, present day theory of switched systems is largely based on assuming certain small but finite time interval termed average dwell time. Thus it appears dominantly characterized by some slow sw itching condition with average dwell time satisfying a certain lower bound, which implies a constraint nonetheless. In cases of nonlinear systems there may well appear non-expected comple xity phenomena of particularly different nature when switching becomes no longer. A fast switching condition with average dwell time satisfying an upper bound is explored and established. A comparison analysis of these innovated characterization s via slightly different overview yielded new results on the tran sient behaviour of switched nonlinear systems, while preserving the system stability. The multiple-Lyapunov functions approac h is used in the analysis and switched systems framework is extended shading new light on the underlying, switching caused system complexities

Robust Full-Order and Reduced- Order Observers for a Class of Uncertain Switched Systems

This paper deals with the problem of robust state estimation for a class of switched linear systems with unknown inputs under average dwell time (ADT) switching, where the switching of the observers is synchronous with that of the estimated system. First, based on the feasibility of an optimization problem with linear matrix inequality (LMI) constraint, a robust sliding-mode switched observer is developed such that the asymptotic state reconstruction is guaranteed even if the switched system is with unknown inputs. Second, a reduced-order switched system which avoids the influence of unknown inputs is constructed by the technique of state transformation, and a reduced-order switched observer is proposed to estimate the continuous states of the original switched system. Next, the conditions under which a full-order switched observer exists also guarantee the existence of a reduced-order switched observer. The convergence of the state estimate is proved to be exponential by appropriate Lyapunov analysis. Finally, the simulation results confirm the predicted performance and applicability by a simplified three-tank system

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results