Showing papers on "Separation principle published in 2011"

Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback

Abstract: This technical note studies synchronization of identical general linear systems on a digraph containing a spanning tree. A leader node or command generator is considered, which generates the desired tracking trajectory. A framework for cooperative tracking control is proposed, including full state feedback control, observer design and dynamic output feedback control. The classical system theory notion of duality is extended to networked systems. It is shown that unbounded synchronization regions that achieve synchronization on arbitrary digraphs containing a spanning tree can be guaranteed by using linear quadratic regulator based optimal control and observer design methods at each node.

Packetized Predictive Control of Stochastic Systems Over Bit-Rate Limited Channels With Packet Loss

Abstract: We study a control architecture for linear time-invariant plants with random disturbances and where a network is placed between the controller output and the plant input. The network imposes a constraint on the expected bit-rate and is affected by random independent and identically distributed (i.i.d.) dropouts. Dropout-rates and acknowledgments of receipt are not available at the controller side. To achieve robustness with respect to i.i.d. dropouts, the controller transmits data packets containing quantized plant input predictions. These are provided by an appropriate optimal entropy coded dithered lattice vector quantizer. Within this context, we derive stochastic stability results and provide a noise-shaping model of the closed loop system. This model is employed for performance analysis by using rate-distortion theory.

A state-space solution to the two-player decentralized optimal control problem

Abstract: In this paper, we present an explicit state-space solution to the two-player decentralized optimal control problem. In this problem, there are two interconnected linear systems that seek to optimize a global quadratic cost. Both controllers perform output feedback, but they have access to different subsets of the available measurements. The optimal controller, which was not previously known, has a state dimension equal to twice the state dimension of the original system.

Robust Output Feedback Control of a Class of Nonlinear Systems Using a Disturbance Observer

Abstract: This paper considers the output-tracking control problem of feedback linearizable nonlinear systems in the presence of external disturbances and modeling errors. A robust output feedback nonlinear controller is designed to achieve excellent output-tracking performance. By exploiting the cascade features of backstepping design, a simple disturbance observer (DOB) is proposed to suppress the effects of the uncertainties, and a high-gain observer (HGOB) is applied to estimate the unmeasureable states of the system. Although the DOB-based controllers are usually designed according to linear control theory, in this study, strict analysis of the nonlinear control system is given. Experimental results on a magnetic levitation system are provided to support the theoretical results and to verify the advantages of the proposed controller.

Optimal Speed Control of Hybrid Electric Vehicles

Abstract: The main objective of this paper is to control the speed of Nonlinear Hybrid Electric Vehicle (HEV) by controlling the throttle position. Various control techniques such as well known Proportional-Integral-Derivative (PID) controller in conjunction with state feedback controller (SFC) such as Pole Placement Technique (PPT), Observer Based Controller (OBC) and Linear Quadratic Regulator (LQR) Controller are designed. Some Intelligent control techniques e.g. fuzzy logic PD, Fuzzy logic PI along with Adaptive Controller such as Self Organizing Controller (SOC) is also designed. The design objective in this research paper is to provide smooth throttle movement, zero steady-state speed error, and to maintain a Selected Vehicle (SV) speed. A comparative study is carried out in order to identify the superiority of optimal control technique so as to get improved fuel economy, reduced pollution, improved driving safety and reduced manufacturing costs.

Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

Abstract: This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness-based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger-type observer within the two degrees-of-freedom control concept. The asymptotic stability of the closed-loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C0-semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.

Nonlinear State-Feedback Dissipation Power Level Control for Nuclear Reactors

Abstract: Power-level regulation is a significant technique for guaranteeing both operation stability and efficiency of nuclear reactors. With the wide application of the digital instrument and control platforms, the implementation of modern state-feedback power control strategies, which have the ability of strengthening both the operation stability and efficiency for nuclear reactors, becomes much easier than before. Due to the advanced property of state-feedback power-level control and nonlinearity of reactor dynamics, it is so meaningful to develop nonlinear state-feedback power-level control laws. In this paper, a novel nonlinear state-feedback dissipation power-level control strategy is presented, which guarantees both the asymptotic closed-loop stability and convergent state-observation. Numerical simulation results show the feasibility and relationship between the observer-gain and control performance, and theoretic analysis corresponding to the simulation results is also given.

Observer-based control of linear complementarity systems

Abstract: In this paper we present observer and output-based controller design methods for linear complementarity systems (LCS) employing a passivity approach Due to various inherent properties of LCS, such as the presence of state jumps, mode dynamics described by differential and algebraic equations (DAEs), and regions for certain modes being lower dimensional, various observer and control design schemes that have been proposed for other classes of (hybrid) dynamical systems do not apply to LCS In particular, we present an observer design method for LCS which is effective even in the presence of state jumps We show the well-posedness of the observer, in the sense of existence and uniqueness of solution trajectories for the estimated state, and prove the global exponential stability of the observation error These two properties guarantee that the estimated state exponentially recovers the state of the system For the problem of stabilization based on output measurements only, we adopt an observer-based control approach in which we apply a state feedback law to the estimated state obtained from the observer We prove that the resulting closed-loop system is well-posed and globally exponentially stable In order to show the well-posedness of the closed loop, novel well-posedness results for LCS based on low-index properties are presented

Stochastic Maximum Principle for Optimal Control Problems of Forward-Backward Systems Involving Impulse Controls

Abstract: We consider a stochastic optimal control problem of a forward-backward system in which the control variable consists of two components: the continuous control and the impulse control. The domain of the control is assumed to be convex. Necessary optimality conditions of the Pontryagin maximum principle type are obtained for this stochastic optimal control problem. We also give additional conditions, under which the necessary optimality conditions turn out to be sufficient.

Pontryagin's maximum principle of optimal control problems with time-delay

Abstract: In this paper, we consider an optimal control problem with time-delay. The state and the control variables contain various constant time-delays. This allows us to represent the necessary conditions in an explicit form. Solution of this problem with infinite terminal time is also given.

Practical exponential stability of perturbed triangular systems and a separation principle

Abstract: In this paper, we present a practical stability result for perturbed dynamic systems depending on a parameter and we study the practical exponential stability of perturbed triangular systems. These results are applied to show that a separation principle for nonlinear uncertain systems can be achieved and which considers practical global uniform exponential stability. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Stability of event-triggered output-feedback control systems

Abstract: This paper focus on the design of the event-triggered control when the full state can not be available. Firstly, an event-triggered control system with a static output-feedback controller is studied. An event condition based on the output error is proposed. The asymptotic stability of the resulting closed-loop system is guaranteed by a condition in terms of an LMI (Linear Matrix Inequality). By solving this LMI, we can design the event condition to obtain longer task periods. Moreover, a corresponding self-triggered control is provided. Furthermore, a state-feedback control system based on an event-triggered observer is researched, where the output of the plant is only transmitted to the observer when the event condition is violated. Conditions in terms of LMIs are derived to ensure the feedback control system as well as the observer error system asymptotic stability. Finally, numerical examples are worked out to illustrate the theoretical results.

The system-matched hold and the intermittent control separation principle

Abstract: An intermittent controller is a form of hybrid controller which adds a generalised sample and hold mechanism to an underlying continuous-time feedback control system. The sampling may be non-uniform or event driven. One particular form of the hold, termed the system-matched hold (SMH) mimics the behaviour of the closed-loop feedback control signal during the intermittent intervals. It is shown in this article that this choice of hold leads to an intermittent separation principle. In particular, this simple analytical result ensures that when using the SMH, the separation properties of the underlying state-estimate feedback control system carry over to the intermittent control system. This separation principle for the SMH has the important consequence that, unlike the zero-order hold case, the stability of the closed-loop system in the fixed sampling case is not dependent on sample interval. It is therefore suggested that the SMH should replace the conventional zero-order hold in circumstances where the sample interval is unknown, time-varying or determined by events.

The maximum principle for partially observed optimal control of forward-backward stochastic systems with random jumps

Abstract: This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.

Separation principle for networked control systems with multiple-packet transmission

Abstract: The authors investigate a class of observer-based discrete-time networked control systems (NCSs) with multiple-packet transmission where random packet dropouts occur independently in both the sensor-to-controller (S/C) and controller-to-actuator (C/A) channels. The authors first propose and prove the separation principle for the NCSs where packet dropouts in the C/A and S/C channels are governed by two independent Markov chains, respectively. Secondly, the authors derive a sufficient condition, in terms of linear matrix inequalities (LMIs), for stabilisation control of the Markov chain-driven NCSs. The authors also derive the necessary and sufficient condition for stabilisation control of the memoryless process-driven NCSs as a special case. A numerical example is provided to illustrate the effectiveness of our method.

Output feedback sliding mode control of a PVTOL including actuators dynamics

Abstract: This paper focuses on the regulation problem of a planar vertical take-off and landing (PVTOL) aircraft using output feedback sliding mode controller where a sliding mode observer is used to estimate the velocity. The observer design is independent of the feedback control design (separation principle). Considering as important the actuators response in the performance of the closed-loop systems, the dynamics of the PVTOL is augmented with the dynamics of the actuators. The performance of the closed-loop system is illustrated through simulation results.

Linear quadratic Gaussian control with quantised innovations Kalman filter over a symmetric channel

Abstract: This study discusses the quantised linear quadratic Gaussian (LQG) control problem for linear stochastic systems. A symmetric channel that connects the sensor and the controller is considered. Given a quantiser that is applied on the most recent innovation of the measurement, it is shown that the well-known separation principle remains valid. Based on a quantised innovations Kalman filter, a suboptimal LQG controller is given in terms of the solutions of two Riccati difference equations associated, respectively, with the state estimation and the standard linear quadratic regulator control. The corresponding approximate suboptimal cost is also derived. An illustrative example is included to demonstrate the effectiveness of the proposed controller.

Robust feedback linearization using higher order sliding mode observer

Abstract: A novel robust feedback linearization scheme is proposed in this paper based on a modified robust exact differentiator. The states and drift terms in the system are estimated simultaneously by the observer using back injection of the control effort. The estimated drift term is used in the feedback loop to compensate the disturbances and observed states are used for feedback linearization. Finite time convergence of the complete closed-loop system is proved and thus a form of separation principle is satisfied, i.e., the controller and observer can be separately designed. The design is verified through simulations and by experiments on a DC motor rig.

On-line identification algorithm and convergence analysis for sandwich systems with backlash

Abstract: In this paper, an on-line algorithm for identification of sandwich systems with backlash is proposed. In this method, the sandwich systems with backlash can be transformed into a special model where all the model parameters are separated based on the so-called key term separation principle. In this case, a piecewise model with linear coefficients combining with nonlinear variables is obtained. Thus, an extended recursive identification algorithm is used to estimate the parameters of the proposed model. Finally, the modeling results on an X-Y positioning stage are presented.

Observer-based pole placement for non-lexicographically-fixed linear time-varying systems

Abstract: In this paper, the observer based pole placement control for non-lexicographically-fixed linear time-varying MIMO systems is considered. Using the concept of the relative degrees of a MIMO system, Ackerman-like design algorithm for pole placement state feedback control is directly derived. This makes the calculation procedure to obtain the pole placement state feedback very simple, especially for MIMO systems. The separation principle is also shown in the case where both of the controllability indices and the observability indices are not lexicographically-fixed.

An SOS-based observer design for polynomial fuzzy systems

Abstract: This paper presents a sum of squares (SOS, for brevity) based observer design for a more general class of polynomial fuzzy systems with the polynomial matrices A i (x(t)) and B i (x(t)) that are permitted to be dependent of the states x(t). First, we briefly summarize previous works on SOS-based observer designs for two limited classes of polynomial fuzzy systems. To overcome the difficulty of the fact that does not realize the so-called separation principle design for the more general class, this paper provides a practical design procedure of a polynomial fuzzy controller and a polynomial fuzzy observer without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy controller and observer designs) and also than the previous SOS-based observer designs. To illustrate the validity of the design approach, a design example is provided. The example shows the utility of our SOS approach to the polynomial fuzzy observer-based control for the more general class of polynomial fuzzy systems.

Non-fragile observer-based H ∞ control for neutral stochastic hybrid systems with time-varying delay

Abstract: The non-fragile observer-based stabilization and H ∞ control problems for neutral stochastic hybrid systems with time-varying delay are studied in this paper. The time-delay is unknown and time-varying with known bounds. Based on Lyapunov functional approach combined with LMIs techniques, the delay-dependent sufficient conditions for the existence of the non-fragile observer-based H ∞ controller are given. Under the control of the non-fragile observer-based H ∞ controller, the resulting closed-loop system not only is robust stochastic exponential stable in the mean square but also satisfies the H ∞ performance level. A numerical example with simulation is given to demonstrate the feasibility and effectiveness of the proposed methods.

A polynomial observer design for a wider class of polynomial fuzzy systems

Abstract: This paper presents a polynomial fuzzy observer design for a wider class of polynomial fuzzy systems via a sum of squares (SOS, for brevity) approach. The proposed SOS-based framework provides a number of innovations and improvements over the existing LMI-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results for a class of polynomial fuzzy systems that is more general representation of the well-known T-S fuzzy system. Next, we propose a polynomial fuzzy observer to estimate states in a wider class of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions is that they realize the so-called separation principle, that is, that a polynomial fuzzy controller and observer for this class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recent developed SOSTOOLS and a semidefinite program (SDP) solver, respectively. To illustrate the validity and applicability of the proposed approach, a design example is provided. The example demonstrates advantages of the SOS-based approach for the existing LMI approaches to T-S fuzzy observer designs.

New approach to an adaptive robust motion controller combined with a disturbance observer

Abstract: Parameter adaptation and disturbance observer (DOB) have been considered as two contrastively different approaches in motion control problems In the authors' previous work, the two techniques were merged into one control design with a theoretically guaranteed performance A drawback of the method is that the controller has to be relatively complicated owing to the interactions between the two mechanisms In this study, by exploiting the cascade features of backstepping design, the DOB is inserted into the position-loop which compensates for the velocity error that may not be suppressed to be sufficiently small by the adaptive mechanism owing to the presence of unparameterised uncertainties This results in a much simpler controller since the two mechanisms are separated Simulation results show that the proposed controller, while being much simpler than the authors' previously proposed controller, yields a comparable control performance