Sliding mode control of constrained nonlinear systems

This technical note introduces the design of sliding mode control algorithms for nonlinear systems in the presence of hard inequality constraints on both control and state variables. Relying on general results on minimum-time higher-order sliding mode for unconstrained systems, a general order control law is formulated to robustly steer the state to the origin, while satisfying all the imposed constraints. Results on minimum-time convergence to the sliding manifold, as well as on the maximization of the domain of attraction, are analytically proved for the first-order and second-order sliding mode cases. A general result is presented regarding the domain of attraction in the general order case, while numerical results on the estimation of the domain of attraction and on minimum-time convergence are discussed for the third-order case, following a procedure applicable to a sliding mode of any order

Hierarchical Model Predictive/Sliding Mode control of nonlinear constrained uncertain systems

This paper presents an overview of some hierarchical control schemes composed by a high level Model Predictive Control (MPC) and a low level Sliding Mode Control (SMC). The latter is realized by using the so-called Integral Sliding Mode (ISM) control approach and is meant to reject the matched disturbances affecting the plant, thus providing a system with reduced uncertainty for the MPC design. Both continuous and discrete-time solutions are discussed in the paper. Moreover, assuming the presence of a network in the control loop, a networked version of the control scheme is presented. It is a model-based event-triggered MPC/ISM control scheme aimed at minimizing the packets transmission. The input-to-state (practical) stability properties of the proposed approaches are also addressed in the paper

An observer-based attitude and nutation control and flexible dynamic analysis for the NASA Magnetospheric Multiscale Mission

Current research with the NASA Goddard Space Flight Center (GSFC) involves the dynamic modeling and control of the NASA Magnetospheric Multiscale (MMS) Mission, a. Solar-Terrestrial Probe mission to study Earth\u27s magnetosphere. Four observer-based attitude and nutrition controllers are designed and evaluated to determine the most effective feedback control system as it applies to MMS. Also, a dynamic analysis of each of the four identical satellites\u27 two Axial Double Probe (ADP) booms is performed to provide an understanding of flexible boom dynamics. The Finite Element method is used in evaluating boom modes of vibration for confirmation of NASA GSFC theoretical analysis and use in flexible model development. The dynamic transient and modal extraction technique are investigated for vibration analysis of constrained and unconstrained bodies. A fully flexible boom and rigid spacecraft model is also developed for vibrational analysis under steady-state rotation and thruster loads. Results indicate, however, the need for future research in numerical analysis of propagating systems through finite element methods and in the stability of the observer-based control system. Linear and nonlinear observers are developed through simulations to estimate satellite attitude and angular body rates without the use of rate sensors. Control systems are then developed assuming perfect state measurements. Euler angles are used to describe satellite attitude in this research. Finally, linear and nonlinear (Sliding Mode Control) techniques are implemented in conjunction with the nonlinear observers to complete the observer-based control system. The results of this research show that, of the methods analyzed, both the Extended Kalman Filter and Sliding Mode Observer implemented with Sliding Mode Control yield the most satisfactory performance. These observer-based control systems both meet NASA design requirements while reducing thruster control effort and reducing the effects of measurement noise and spacecraft uncertainties/disturbances. More simulations, however, are needed to verify performance of the proposed observer-based control system over all possible ranges of operation

Adaptive Sliding Mode Observer for Nonlinear Interconnected Systems with Time Varying Parameters

In this paper, a class of nonlinear interconnected systems with uncertain time varying parameters (TVPs) is considered. Both the interconnections and the isolated subsystems are nonlinear. Sliding mode control method and adaptive techniques are employed together to design an observer to estimate the state variables of the systems in presence of unknown TVPs. The Lyapunov direct method is used to analysis the stability of the sliding motion and it is not required to solve the so-called constrained Lyapunov problem (CLP). A set of conditions is developed under which the augmented systems formed by the error dynamical systems and the designed adaptive laws, are globally uniformly ultimately bounded. A simulation example is presented and the results show that the method proposed in this paper is effective

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Sliding Mode Reference Coordination of Constrained Feedback Systems

[EN] This paper addresses the problem of coordinating dynamical systems with possibly different dynamics (e.g., linear and nonlinear, different orders, constraints, etc.) to achieve some desired collective behavior under the constraints and capabilities of each system. To this end, we develop a new methodology based on reference conditioning techniques using geometric set invariance and sliding mode control: the sliding mode reference coordination (SMRCoord). The main idea is to coordinate the systems references. Starting from a general framework, we propose two approaches: a local one through direct interactions between the different systems by sharing and conditioning their own references and a global centralized one, where a central node makes decisions using information coming from the systems references. In particular, in this work we focus in implementation on multivariable systems like unmanned aerial vehicles (UAVs) and robustness to external perturbations. To show the applicability of the approach, the problem of coordinating UAVs with input constraints is addressed as a particular case of multivariable reference coordination with both global and local configuration.Research in this area is partially supported by Argentine government (ANPCyT PICT 2011-0888 and CONICET PIP 112-2011-00361), Spanish government (FEDER-CICYT DPI2011-28112-C04-01), and Universitat Politecnica de Valencia (Grant FPI/2009-21)Vignoni, A.; Garelli, F.; Picó, J. (2013). Sliding Mode Reference Coordination of Constrained Feedback Systems. Mathematical Problems in Engineering. 2013:1-11. https://doi.org/10.1155/2013/764348S1112013Information consensus in multivehicle cooperative control. (2007). IEEE Control Systems, 27(2), 71-82. doi:10.1109/mcs.2007.338264Cao, Y., Yu, W., Ren, W., & Chen, G. (2013). An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination. IEEE Transactions on Industrial Informatics, 9(1), 427-438. doi:10.1109/tii.2012.2219061Interconnected dynamic systems: An overview on distributed control. (2013). IEEE Control Systems, 33(1), 76-88. doi:10.1109/mcs.2012.2225929Olfati-Saber, R., Fax, J. A., & Murray, R. M. (2007). Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of the IEEE, 95(1), 215-233. doi:10.1109/jproc.2006.887293He, W., & Cao, J. (2011). Consensus control for high-order multi-agent systems. IET Control Theory & Applications, 5(1), 231. doi:10.1049/iet-cta.2009.0191Liu, L. (2012). Robust cooperative output regulation problem for non-linear multi-agent systems. IET Control Theory & Applications, 6(13), 2142-2148. doi:10.1049/iet-cta.2011.0575Pitarch, J. L., Sala, A., & Arino, C. V. (2014). Closed-Form Estimates of the Domain of Attraction for Nonlinear Systems via Fuzzy-Polynomial Models. IEEE Transactions on Cybernetics, 44(4), 526-538. doi:10.1109/tcyb.2013.2258910Nuñez, S., De Battista, H., Garelli, F., Vignoni, A., & Picó, J. (2013). Second-order sliding mode observer for multiple kinetic rates estimation in bioprocesses. Control Engineering Practice, 21(9), 1259-1265. doi:10.1016/j.conengprac.2013.03.003Wu, L., Su, X., & Shi, P. (2012). Sliding mode control with bounded gain performance of Markovian jump singular time-delay systems. Automatica, 48(8), 1929-1933. doi:10.1016/j.automatica.2012.05.064Cao, Y., Ren, W., & Meng, Z. (2010). Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking. Systems & Control Letters, 59(9), 522-529. doi:10.1016/j.sysconle.2010.06.002Cortés, J. (2006). Finite-time convergent gradient flows with applications to network consensus. Automatica, 42(11), 1993-2000. doi:10.1016/j.automatica.2006.06.015Rao, S., & Ghose, D. (2011). Sliding mode control-based algorithms for consensus in connected swarms. International Journal of Control, 84(9), 1477-1490. doi:10.1080/00207179.2011.602834Guo, P., Zhang, J., Lyu, M., & Bo, Y. (2013). Sliding Mode Control for Multiagent System with Time-Delay and Uncertainties: An LMI Approach. Mathematical Problems in Engineering, 2013, 1-12. doi:10.1155/2013/805492Garelli, F., Mantz, R. J., & De Battista, H. (2006). Limiting interactions in decentralized control of MIMO systems. Journal of Process Control, 16(5), 473-483. doi:10.1016/j.jprocont.2005.09.001Garelli, F., Mantz, R. J., & De Battista, H. (2007). Sliding mode compensation to preserve dynamic decoupling of stable systems. Chemical Engineering Science, 62(17), 4705-4716. doi:10.1016/j.ces.2007.05.020Picó, J., Garelli, F., De Battista, H., & Mantz, R. J. (2009). Geometric invariance and reference conditioning ideas for control of overflow metabolism. Journal of Process Control, 19(10), 1617-1626. doi:10.1016/j.jprocont.2009.08.007Revert, A., Garelli, F., Pico, J., De Battista, H., Rossetti, P., Vehi, J., & Bondia, J. (2013). Safety Auxiliary Feedback Element for the Artificial Pancreas in Type 1 Diabetes. IEEE Transactions on Biomedical Engineering, 60(8), 2113-2122. doi:10.1109/tbme.2013.2247602Gracia, L., Sala, A., & Garelli, F. (2012). A supervisory loop approach to fulfill workspace constraints in redundant robots. Robotics and Autonomous Systems, 60(1), 1-15. doi:10.1016/j.robot.2011.07.008Gracia, L., Garelli, F., & Sala, A. (2013). Integrated sliding-mode algorithms in robot tracking applications. Robotics and Computer-Integrated Manufacturing, 29(1), 53-62. doi:10.1016/j.rcim.2012.07.007Vignoni, A., Garelli, F., & Picó, J. (2013). Coordinación de sistemas con diferentes dinámicas utilizando conceptos de invarianza geométrica y modos deslizantes. Revista Iberoamericana de Automática e Informática Industrial RIAI, 10(4), 390-401. doi:10.1016/j.riai.2013.09.001Hanus, R., Kinnaert, M., & Henrotte, J.-L. (1987). Conditioning technique, a general anti-windup and bumpless transfer method. Automatica, 23(6), 729-739. doi:10.1016/0005-1098(87)90029-xMareczek, J., Buss, M., & Spong, M. W. (2002). Invariance control for a class of cascade nonlinear systems. IEEE Transactions on Automatic Control, 47(4), 636-640. doi:10.1109/9.995041Blasco, X., García-Nieto, S., & Reynoso-Meza, G. (2012). Control autónomo del seguimiento de trayectorias de un vehículo cuatrirrotor. Simulación y evaluación de propuestas. Revista Iberoamericana de Automática e Informática Industrial RIAI, 9(2), 194-199. doi:10.1016/j.riai.2012.01.00

Asynchronous networked MPC with ISM for uncertain nonlinear systems

A model-based event-triggered control scheme for nonlinear constrained continuous-time uncertain systems in networked configuration is presented in this paper. It is based on the combined use of Model Predictive Control (MPC) and Integral Sliding Mode (ISM) control, and it is oriented to reduce the packets transmission over the network both in the direct path and in the feedback path, in order to avoid network congestion. The key elements of the proposed control scheme are the ISM local control law, the MPC remote controller, a smart sensor and a smart actuator, both containing a copy of the nominal model of the plant. The role of the ISM control law is to compensate matched uncertainties, without amplifying the unmatched ones. The MPC controller with tightened constraints generates the control component oriented to comply with state and control requirements, and is asynchronous since the underlying constrained optimization problem is solved only when a triggering event occurs. In the paper, the robustness properties of the controlled system are theoretically analyzed, proving the regional input-tostate practical stability of the overall control scheme

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 ∞ 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

Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey

Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany