Muhammad Rehan

Modeling and automatic feedback control of tremor: adaptive estimation of deep brain stimulation.

This paper discusses modeling and automatic feedback control of (postural and rest) tremor for adaptive-control-methodology-based estimation of deep brain stimulation (DBS) parameters. The simplest linear oscillator-based tremor model, between stimulation amplitude and tremor, is investigated by utilizing input-output knowledge. Further, a nonlinear generalization of the oscillator-based tremor model, useful for derivation of a control strategy involving incorporation of parametric-bound knowledge, is provided. Using the Lyapunov method, a robust adaptive output feedback control law, based on measurement of the tremor signal from the fingers of a patient, is formulated to estimate the stimulation amplitude required to control the tremor. By means of the proposed control strategy, an algorithm is developed for estimation of DBS parameters such as amplitude, frequency and pulse width, which provides a framework for development of an automatic clinical device for control of motor symptoms. The DBS parameter estimation results for the proposed control scheme are verified through numerical simulations.

Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen’s inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust against norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

Static and low order anti-windup synthesis for cascade control systems with actuator saturation: an application to temperature-based process control.

In this paper, a new framework for designing static and low order anti-windup compensator (AWC) for industrial cascade control systems with actuator saturation constraint is presented. Based on less conservative block diagonal quadratic Lyapunov function, sector boundedness, decoupled architecture, L(2) norm reduction and cascade loop compensation, linear matrix inequalities are developed which guarantee stability and suitable performance for overall closed-loop system. Static AWC parameters are obtained by comparing the full order AWC architecture with generalized architecture for cascade control system. Low order AWC is designed by sub-optimal approach in which AWC weights are tuned by designer. Anti-windup compensator is divided into inner and outer loop compensators which compensate the effect of saturation at each level. It is observed that the proposed methodology is less conservative than the traditional AWC schemes when applied to cascade control systems. The proposed scheme is successfully tested experimentally on a temperature-based process control system and results are outlined.

A novel anti-windup framework for cascade control systems: an application to underactuated mechanical systems.

This paper describes the anti-windup compensator (AWC) design methodologies for stable and unstable cascade plants with cascade controllers facing actuator saturation. Two novel full-order decoupling AWC architectures, based on equivalence of the overall closed-loop system, are developed to deal with windup effects. The decoupled architectures have been developed, to formulate the AWC synthesis problem, by assuring equivalence of the coupled and the decoupled architectures, instead of using an analogy, for cascade control systems. A comparison of both AWC architectures from application point of view is provided to consolidate their utilities. Mainly, one of the architecture is better in terms of computational complexity for implementation, while the other is suitable for unstable cascade systems. On the basis of the architectures for cascade systems facing stability and performance degradation problems in the event of actuator saturation, the global AWC design methodologies utilizing linear matrix inequalities (LMIs) are developed. These LMIs are synthesized by application of the Lyapunov theory, the global sector condition and the ℒ2 gain reduction of the uncertain decoupled nonlinear component of the decoupled architecture. Further, an LMI-based local AWC design methodology is derived by utilizing a local sector condition by means of a quadratic Lyapunov function to resolve the windup problem for unstable cascade plants under saturation. To demonstrate effectiveness of the proposed AWC schemes, an underactuated mechanical system, the ball-and-beam system, is considered, and details of the simulation and practical implementation results are described.

Robust Synchronization of Delayed Chaotic FitzHugh-Nagumo Neurons under External Electrical Stimulation

Synchronization of chaotic neurons under external electrical stimulation (EES) is studied in order to understand information processing in the brain and to improve the methodologies employed in the treatment of cognitive diseases. This paper investigates the dynamics of uncertain coupled chaotic delayed FitzHugh-Nagumo (FHN) neurons under EES for incorporated parametric variations. A global nonlinear control law for synchronization of delayed neurons with known parameters is developed. Based on local and global Lipschitz conditions, knowledge of the bounds on the neuronal states, the Lyapunov-Krasovskii functional, and the L 2 gain reduction, a less conservative local robust nonlinear control law is formulated to address the problem of robust asymptotic synchronization of delayed FHN neurons under parametric uncertainties. The proposed local control law guarantees both robust stability and robust performance and provides the L 2 bound for uncertainty rejection in the synchronization error dynamics. Separate conditions for single-input and multiple-input control schemes for synchronization of a wide class of FHN systems are provided. The results of the proposed techniques are verified through numerical simulations.

On observer-based control of one-sided Lipschitz systems

Abstract This paper describes the novel observer-based controller design for the one-sided Lipschitz nonlinear systems. An observer-based controller design condition is obtained by application of the Lyapunov theory, by involving the one-sided Lipschitz condition and quadratic inner-boundedness criterion, and by incorporating the matrix inequality procedures. Further, a decoupling condition, necessary and sufficient for the main design approach, is developed to determine the controller and observer gains. Furthermore, two design conditions, a computationally simple sufficient condition and a more generic necessary and sufficient condition, based on the existing and the novel treatments for the one-sided Lipchitz nonlinearity are evaluated to obtain the observer-based control solution. An algorithm for solving the proposed design constraints by combining a nested bilinear-terms-solver approach and a nonlinear-optimization-based cone complementary linearization method is provided. The effectiveness of the proposed observer-based controller design for the one-sided Lipschitz nonlinear systems is demonstrated using a numerical example.

Observer-based robust control of one-sided Lipschitz nonlinear systems

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Youngs inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.

Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

Observer-based control of nonlinear systems under input-output delays is studied.Time-varying nature of delays is incorporated for the controller design.Delay-range-dependent observer-based control is reported.Decoupling technique is applied to compute controller and observer gains.The control scheme is tested to control a one-link flexible joint robotic arm. The problem of designing observer-based controller for a class of nonlinear time-delay systems subjected to input and output time-varying delays is addressed in this paper. More incisively, a delay-range-dependent criterion, incorporating variation of delays between known lower and upper bounds, is established for control of nonlinear time-delay systems. The proposed methodology ensures asymptotic stability of the closed-loop systems state and the estimation error between states of the system and observer. By application of a Lyapunov-Krasovskii functional, Jensens inequality, standard matrix inequality procedures, Luenberger-type observer, delay-interval bounds and delay-derivative limits, observer-based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time-delay systems is provided. Further, a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis. A novel observer-based control scheme for the linear time-delay systems with interval time-varying input as well as output lags is derived from the proposed control strategy. The traditional delay-dependent controller design, incorporating zero lower bound of the delay, for the time-delay systems is a particular scenario of the projected delay-range-dependent approach. The proposed decoupled observer-based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach. Finally, a numerical simulation example of control of one-link flexible joint robotic arm is provided to verify the proposed design methodology.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies.

Synchronization of Coupled Different Chaotic FitzHugh-Nagumo Neurons with Unknown Parameters under Communication-Direction-Dependent Coupling

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.