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Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses
This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an â sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed â noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant
GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the
Alexander von Humboldt Foundation of German
Adaptive Discrete Second Order Sliding Mode Control with Application to Nonlinear Automotive Systems
Sliding mode control (SMC) is a robust and computationally efficient
model-based controller design technique for highly nonlinear systems, in the
presence of model and external uncertainties. However, the implementation of
the conventional continuous-time SMC on digital computers is limited, due to
the imprecisions caused by data sampling and quantization, and the chattering
phenomena, which results in high frequency oscillations. One effective solution
to minimize the effects of data sampling and quantization imprecisions is the
use of higher order sliding modes. To this end, in this paper, a new
formulation of an adaptive second order discrete sliding mode control (DSMC) is
presented for a general class of multi-input multi-output (MIMO) uncertain
nonlinear systems. Based on a Lyapunov stability argument and by invoking the
new Invariance Principle, not only the asymptotic stability of the controller
is guaranteed, but also the adaptation law is derived to remove the
uncertainties within the nonlinear plant dynamics. The proposed adaptive
tracking controller is designed and tested in real-time for a highly nonlinear
control problem in spark ignition combustion engine during transient operating
conditions. The simulation and real-time processor-in-the-loop (PIL) test
results show that the second order single-input single-output (SISO) DSMC can
improve the tracking performances up to 90%, compared to a first order SISO
DSMC under sampling and quantization imprecisions, in the presence of modeling
uncertainties. Moreover, it is observed that by converting the engine SISO
controllers to a MIMO structure, the overall controller performance can be
enhanced by 25%, compared to the SISO second order DSMC, because of the
dynamics coupling consideration within the MIMO DSMC formulation.Comment: 12 pages, 7 figures, 1 tabl
Variance-constrained multiobjective control and filtering for nonlinear stochastic systems: A survey
The multiobjective control and filtering problems for nonlinear stochastic systems with variance constraints are surveyed. First, the concepts of nonlinear stochastic systems are recalled along with the introduction of some recent advances. Then, the covariance control theory, which serves as a practical method for multi-objective control design as well as a foundation for linear system theory, is reviewed comprehensively. The multiple design requirements frequently applied in engineering practice for the use of evaluating system performances are introduced, including robustness, reliability, and dissipativity. Several design techniques suitable for the multi-objective variance-constrained control and filtering problems for nonlinear stochastic systems are discussed. In particular, as a special case for the multi-objective design problems, the mixed H 2 / H â control and filtering problems are reviewed in great detail. Subsequently, some latest results on the variance-constrained multi-objective control and filtering problems for the nonlinear stochastic systems are summarized. Finally, conclusions are drawn, and several possible future research directions are pointed out
Scaled bilateral teleoperation using discrete-time sliding mode controller
In this paper, the design of a discrete-time slidingmode
controller based on Lyapunov theory is presented along
with a robust disturbance observer and is applied to a piezostage
for high-precision motion. A linear model of a piezostage was
used with nominal parameters to compensate the disturbance
acting on the system in order to achieve nanometer accuracy. The
effectiveness of the controller and disturbance observer is validated
in terms of closed-loop position performance for nanometer
references. The control structure has been applied to a scaled
bilateral structure for the custom-built telemicromanipulation
setup. A piezoresistive atomic force microscope cantilever with a
built-in Wheatstone bridge is utilized to achieve the nanonewtonlevel
interaction forces between the piezoresistive probe tip and
the environment. Experimental results are provided for the
nanonewton-range force sensing, and good agreement between
the experimental data and the theoretical estimates has been
demonstrated. Force/position tracking and transparency between
the master and the slave has been clearly demonstrated after
necessary scalin
Robust Simulation for Hybrid Systems: Chattering Path Avoidance
The sliding mode approach is recognized as an efficient tool for treating the
chattering behavior in hybrid systems. However, the amplitude of chattering, by
its nature, is proportional to magnitude of discontinuous control. A possible
scenario is that the solution trajectories may successively enter and exit as
well as slide on switching mani-folds of different dimensions. Naturally, this
arises in dynamical systems and control applications whenever there are
multiple discontinuous control variables. The main contribution of this paper
is to provide a robust computational framework for the most general way to
extend a flow map on the intersection of p intersected (n--1)-dimensional
switching manifolds in at least p dimensions. We explore a new formulation to
which we can define unique solutions for such particular behavior in hybrid
systems and investigate its efficient computation/simulation. We illustrate the
concepts with examples throughout the paper.Comment: The 56th Conference on Simulation and Modelling (SIMS 56), Oct 2015,
Link\"oping, Sweden. 2015, Link\"oping University Pres
Adaptive Backstepping Controller Design for Stochastic Jump Systems
In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques
Cooling panel wall system with difference types of cooling mediums
Global warming has caused worldwide average surface temperature to rise about 0.74oC during the past 100 years, which is partly aggravated by air-conditioning that releases chlorofluorocarbons (CFCs) and forming a vicious cycle. This paper proposes a cooling house system that can promote thermal comfort in buildings without air-conditioning. The cooling panel wall forms a part of an Integrated Building System (IBS), and is essentially made of tubes filled with either water or glycerin as the coolant. Target strength for the panel wall was designed based on the Malaysian Standard (MS) while the building ventilation system followed the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) standard. The results are reported based on indoor and outdoor temperature difference together with relative humidity to identify the best performing house model and also coolant. The outcome of this research is expected to add value to heritage house design concepts with a better promotion of air flow and circulation in the building, without over-usage of natural resources and higher building cost to achieve the same objective
Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities
An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated
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