H_∞ Static Output-Feedback Gain-Scheduled Control for Discrete LPV Time-Delay Systems^⁎

This paper proposes new synthesis conditions to design H∞ static output-feedback controllers for discrete-time linear systems affected by time-varying parameters and time-varying delays. The design conditions are provided in terms of sufficient parameter-dependent linear matrix inequalities with a scalar parameter, being capable of synthesizing either robust or gain-scheduled controllers. The main motivations to deal with such problem are that many real-world plants can be modeled in terms of discrete-time linear parameter-varying (LPV) time-delay models and the lack of methods to deal with such systems considering an output-feedback based approach. The technique presented in this paper is quite generalist, allowing an arbitrary structure for the measured output matrix. Numerical examples are provided to illustrate the effectiveness of the synthesis conditions, tractable in terms of LMI relaxations, for robust or gain-scheduled H∞ output-feedback for LPV time-delayed systems

Fixed-structure H-2 controller design for polytopic systems via LMIs

In this paper a new approach for fixed-structure H2 controller design in terms of solutions to a set of linear matrix inequalities are given. Both discrete- and continuous-time single-input single-output (SISO) time- invariant systems are considered. Then the results are extended to systems with polytopic uncertainty. The presented methods are based on an inner convex approximation of the non-convex set of fixed-structure H2 controllers. The designed procedures initialized either with a stable polynomial or with a stabilizing controller. An iterative procedure for robust controller design is given that converges to a suboptimal solution. The monotonic decreasing of the upper bound on the H2 norm is established theoretically for both nominal and robust controller design

An LMI-based local search algorithm to compute stabilizing feedback gains directly as optimization variables

Orientador: Ricardo Coração de Leão Fontoura de OliveiraDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta dissertação trata do problema de estabilização robusta de sistemas lineares incertos por realimentação estática de estados e de saídas. São investigados sistemas contínuos e discretos no tempo, com as matrizes do sistema pertencendo a um domínio politópico. Diferentemente dos métodos de estabilização robusta disponíveis na literatura, nos quais o produto entre a matriz de Lyapunov (ou a variável de folga) e o ganho de controle é transformado em uma nova variável, nesta dissertação é proposto um novo paradigma, evitando a mudança de variável e fornecendo condições de síntese que tratam o ganho de controle diretamente como uma variável de otimização. O procedimento de síntese é formulado em termos de um algoritmo iterativo com convergência local baseado em desigualdades matriciais lineares, tendo como principais novidades os seguintes pontos: tanto a matriz de Lyapunov como a matriz dinâmica de malha fechada aparecem de forma afim nas condições; apenas variáveis de folga são fixas a cada iteração, evitando a alternância clássica entre a matriz de Lyapunov e o ganho de controle; inicialização independente das matrizes do sistema, garantindo a existência de soluções factíveis a cada iteração; critério de parada baseado em uma condição de análise de estabilidade robusta. Comparações numéricas exaustivas mostram que o método proposto apresenta eficácia maior que todos os métodos da literatura, sendo especialmente adequado para tratar os problemas de realimentação de saída e controle descentralizadoAbstract: This dissertation addresses the problem of robust stabilization of uncertain linear sys-tems by static state- and output-feedback control laws. Continuous- and discrete-time systems with matrices belonging to a polytopic domain are investigated. Differently from the robust stabilization methods available in the literature, where the product between the Lyapunov matrix (or slack variable) and the control gain is transformed into a new variable, in this dissertation a new paradigm is proposed, avoiding the change of variable and providing synthesis conditions that handle the control gain directly as an optimization variable. The synthesis procedure is formulated in terms of a locally convergent iterative algorithm based on linear matrix inequalities, with the following points as main novelties: both the Lyapunov and closed-loop dynamic matrices appear affinely in the conditions; only slack variables are fixed at each iteration, avoiding the classic alternation between the Lyapunov matrix and the control gain; initialization independent of the matrices of the system, ensuring the existence of feasible solutions at each iteration; stopping criterion based on a robust stability analysis condition. Exhaustive numerical comparisons show that the proposed method can outperform all the conditions from the literature in terms of effectiveness, being specially suitable to deal with output-feedback and decentralized control problemsMestradoAutomaçãoMestre em Engenharia Elétric

Regeneratively and Passively Constrained Control of Vibratory Networks

This dissertation is focused on the control of vibratory networks. Mechanical examples of vibratory systems include a civil structure, automobile, and a cantilever beam. These systems are excited by external disturbances such as earthquakes, wind, or uneven road elevations. Both passive and active control laws can be utilized to suppress vibrations in these networks. Each type of control law possesses inherent advantages and drawbacks. Active control provides the highest performance but is expensive, relies on an external power source, and is complicated to implement and maintain. Passive control devices (composed of springs, inertial elements, dashpots) represent the cheapest option and provide energy-autonomy, but have inferior performance when compared to an active control device. Due to their reliability and low cost, passive control technologies set the baseline for comparison for other, more sophisticated technologies. On the other hand, although it yields superior performance, active control presumes availability of unlimited energy, which may be an impractical or unreliable assumption. This dissertation examines a new class of control technologies, called regenerative control systems. A regenerative control system theoretically possesses energy-autonomy, but does so with better performance when compared to a passive control system. However, regenerative control devices are more expensive than passive and therefore the improved performance they attain must warrant utilization. A regenerative control device is assumed to be connected to a large energy storage device (battery, supercapacitor, etc). At times, the control device will draw energy from the energy storage device in order to actuate the network. At other times, the control device converts mechanical energy from the network into electrical energy and replenishes the energy in the storage device. The regenerative controller is constrained such that, on average, it generates more energy than it expends. This constraint, which is a relaxation of a passive control law constraint, ensures the local energy storage device never completely depletes. One of the main focuses of this research is to develop theory which can can solve for optimal regenerative and passive control laws. Optimizing control laws for both types of technology, in the context of the same problem, allows for a fair comparison.The regenerative control design problem can be formulated as a convex optimization and therefore can be solved easily with many commercial solvers. Passively constrained control design is a nonconvex problem and a new technique, Iterative Convex Over-Bounding (ICO) is proposed and developed to solve this nonconvex optimization. We show that optimal regenerative control outperforms optimal passive control if parasitic losses are sufficiently small. We also propose a technique to quantify how large the parasitics can be for a regenerative controller to still outperform a passive controller for a given problem.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138455/1/erwarner_1.pd

Robust control and filtering design for discrete-time linear systems with dynamics enhancement

Orientador: Pedro Luis Dias PeresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta tese investiga os problemas de síntese de controladores robustos por realimentação estática de estados e de saída e de projeto de filtros robustos para sistemas incertos discretos lineares e invariantes no tempo por meio do enriquecimento da dinâmica do sistema. Considera-se que informações passadas estejam presentes nas leis de controle e, também, que a estrutura do filtro tenha dimensão superior à dimensão do sistema sendo filtrado. Extensões para abordar o problema de smoothing são igualmente propostas. O procedimento de síntese dos controladores e filtros é realizado construindo-se um sistema auxiliar aumentado, a partir do qual condições convexas para a síntese são derivadas, sendo essas descritas em termos de Desigualdades Matriciais Lineares dependentes de parâmetros. As normas H-2 e H-infinito são utilizadas como critérios de desempenho para as metodologias desenvolvidas. As condições propostas exploram a estrutura particular do sistema auxiliar aumentado, sendo distintas das condições clássicas da literatura para projeto de filtros robustos de ordem completa ou para o cômputo do ganho de realimentação de estado ou de saída para o sistema aumentado em função apenas do instante atual. Demonstra-se que os métodos propostos englobam outras técnicas disponíveis na literatura, não possuindo, portanto, maior grau de conservadorismo do que as abordagens existentes. Exemplos numéricos são apresentados para ilustrar as vantagens das condições desenvolvidas na determinação de menores limitantes para as normas H-2 e H-infinito, mostrando que o método tende a ser menos conservador conforme mais informações passadas são agregadas às leis de controle ou à medida que a ordem dos filtros aumenta. Outrossim, os exemplos numéricos evidenciam que os mesmos resultados não são obtidos pela simples aplicação de técnicas convencionais da literatura ao sistema auxiliar aumentadoAbstract: This thesis is concerned with the problems of robust static state and output feedback control synthesis and of robust filtering design for uncertain linear discrete time-invariant systems by means of dynamics enhancement. For that, the control laws are supposed to contain past information and the filter structure has a dimension greater than the dimension of the system being filtered. Extensions to cope with the smoothing problem are proposed as well. The procedure for the design of controllers and filters is performed by defining an auxiliary augmented system, from which convex synthesis conditions are derived, being described in terms of parameter-dependent Linear Matrix Inequalities. The H-2 and H-infinity norms are used as performance criteria for the developed methodology. The proposed conditions explore the particular structure of the auxiliary augmented system, thus being distinct from classical conditions from the literature for robust full-order filtering design, or for determining the state- or the output-feedback gains for the augmented system, in terms solely of the current instant. It is shown that the proposed methods encompass other techniques available in the literature, not incurring, therefore, in a greater degree of conservatism than the existing approaches. Numerical examples illustrate the advantages of the proposed conditions in determining lower upper-bounds for the H-2 and H-infinity norms, showing that the method tends to be less conservative as more past information is added to the control laws or as the order of the filters increases. Furthermore, the numerical examples evince that the same results are not attained by simply applying standard approaches from the literature to the auxiliary augmented systemDoutoradoAutomaçãoDoutor em Engenharia Elétrica2013/05957-1, 2014/23074-2FAPES

Lmi Relaxations For Reduced-order Robust H ∞ Control Of Continuous-time Uncertain Linear Systems

This technical note is concerned with the problem of reduced order robust H ∞ dynamic output feedback control design for uncertain continuous-time linear systems. The uncertain time-invariant parameters belong to a polytopic domain and affect all the system matrices. The search for a reduced-order controller is converted in a problem of static output feedback control design for an augmented system. To solve the problem, a two-stage linear matrix inequality (LMI) procedure is proposed. At the first step, a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined. This parameter-dependent state feedback controller is used at the second stage, which synthesizes the robust (parameter- independent) output feedback H ∞ dynamic controller. A homogeneous polynomially parameter-dependent Lyapunov function of arbitrary degree is used to assess closed-loop stability with a prescribed H ∞ attenuation level. As illustrated by numerical examples, the proposed method provides better results than other LMI based conditions from the literature. © 2011 IEEE.57615321537Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback-A survey (1997) Automatica, 33 (2), pp. 125-137. , FebBlondel, V.D., Tsitsiklis, J.N., A survey of computational complexity results in systems and control (2000) Automatica, 36 (9), pp. 1249-1274. , SepFu, M., Luo, Z.-Q., Computational complexity of a problem arising in fixed order output feedback design (1997) Systems and Control Letters, 30 (5), pp. 209-215. , PII S0167691197000145Peres, P.L.D., Geromel, J.C., An alternate numerical solution to the linear quadratic problem (1994) IEEE Trans. Autom. 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Control, 48 (5), pp. 866-872. , MayGeromel, J.C., Korogui, R.H., Bernussou, J., Robust output feedback control for continuous time polytopic systems (2007) IET Control Theory Appl., 1 (5), pp. 1541-1549. , SepYaesh, I., Shaked, U., Robust reduced-order output-feedback control (2009) Proc. 6th IFAC Symp. Robust Control Design, Haifa, Israel, pp. 155-160. , JunTrofino, A., Sufficient LMI conditions for the design of static and reduced order controllers (2009) Proc. 48th IEEE Conf. Decision Control-28th Chinese Control Conf., pp. 6668-6673. , Shanghai, China DecHenrion, D., Lasserre, J.-B., Convergent relaxations of polynomial matrix inequalities and static output feedback (2006) IEEE Transactions on Automatic Control, 51 (2), pp. 192-202. , DOI 10.1109/TAC.2005.863494Apkarian, P., Noll, D., Nonsmooth synthesis (2006) IEEE Trans. Autom. 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H∞ Dynamic Output Feedback For Lpv Systems Subject To Inexactly Measured Scheduling Parameters

This paper proposes a design procedure for reduced-order dynamic output feedback (DOF) gain-scheduling controllers with H∞ guaranteed cost for linear parameter-varying (LPV) continuous-time systems, where the measurement of the scheduling parameters may be affected by uncertainties. Thanks to the flexibility of the proposed modeling, the LPV-DOF controllers can be implemented in terms of a selected set of parameters, which are supposed to be available for measurement in real time. The design conditions can cope with both additive and multiplicative noises, considered as time-varying uncertainties, affecting the measures. All parameters and uncertainties are modeled through the multi-simplex framework, i.e., the Cartesian product of simplexes. The problem is solved through a two-stage procedure based on linear matrix inequalities. © 2013 AACC American Automatic Control Council.60606065Boeing,Eaton,Halliburton,Honeywell,MathWorksLee, H.C., Choi, J.W., Ackermann-like eigenvalue assignment formulae for linear time-varying systems (2005) IEE Proc. - Control Theory and Appl, 152 (4), pp. 427-434. , JulyEl Ghaoui, L., Niculescu, S.I., (2000) Advances in Linear Matrix Inequality Methods in Control, Ser. Advances in Design and Control, , Philadelphia, PA: SIAMMontagner, V.F., Oliveira, R.C.L.F., Leite, V.J.S., Peres, P.L.D., LMI approach for Hlinear parameter-varying state feedback control (2005) IEE Proc. - Control Theory and Appl, 152 (2), pp. 195-201. , MarchGeromel, J.C., Colaneri, P., Robust stability of time varying polytopic systems (2006) Syst. Control Letts, 55 (1), pp. 81-85. , JanuaryLöfberg, J., YALMIP: A toolbox for modeling and optimization in MATLAB (2004) Proc. 2004 IEEE Int. Symp. on Comput. Aided Control Syst. des, pp. 284-289. , http://control.ee.ethz.ch/~joloef/yalmip.php, Taipei, Taiwan, SeptemberSturm, J.F., Using SeDuMi 1. 02, a MATLAB toolbox for optimization over symmetric cones (1999) Optim. Method Softw, 11 (1-4), pp. 625-653. , http://sedumi.ie.lehigh.edu/Packard, A., Gain scheduling via linear fractional transformations (1994) Syst. Control Letts, 22 (2), pp. 79-92. , FebruaryLeith, D.J., Leithead, W.E., Survey of gain-scheduling analysis and design (2000) Int. J. Control, 73 (11), pp. 1001-1025. , JulyMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Design of Hgain-scheduled controllers for linear time-varying systems by means of polynomial Lyapunov functions (2006) Proc. 45th IEEE Conf. Decision Control, pp. 5839-5844. , San Diego, CA, USA, DecemberMontagner, V.F., Oliveira, R.C.L.F., Peres, P.L.D., Bliman, P.-A., Stability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variations (2009) Int. J. Control, 82 (6), pp. 1045-1059. , JuneKöse, I.E., Jabbari, F., Control of LPV systems with partly measured parameters (1999) IEEE Trans. Autom. Control, 44 (3), pp. 658-663. , MarchDaafouz, J., Bernussou, J., Geromel, J.C., On inexact LPV control design of continuous-time polytopic systems (2008) IEEE Trans. Autom. Control, 53 (7), pp. 1674-1678. , AugustSato, M., Ebihara, Y., Peaucelle, D., Gain-scheduled state-feedback controllers using inexactly measured scheduling parameters: H2 and Hproblems (2010) Proc. 2010 Amer. Control Conf, pp. 3094-3099Peaucelle, D., Arzelier, D., An efficient numerical solution for H2 static output feedback synthesis (2001) Proc. 2001 Eur. Control Conf, pp. 3800-3805. , Porto, Portugal, SeptemberArzelier, D., Peaucelle, D., Salhi, S., Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound (2003) Proc. 4th IFAC Symp. Robust Control Design, pp. 425-430. , Milan, Italy, JuneMehdi, D., Boukas, E.K., Bachelier, O., Static output feedback design for uncertain linear discrete time systems (2004) IMA J. Math. Control Inform, 21 (1), pp. 1-13. , MarchArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design (2010) Proc. 2010 Amer. Control Conf, pp. 4683-4688. , Baltimore, MD, USA, June-JulyAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Robust Hstatic output-feedback design for time-invariant discrete-time polytopic systems from parameter-dependent state-feedback gains (2010) Proc. 2010 Amer. Control Conf, pp. 4677-4682. , Baltimore, MD, USA, June-JulyAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., Static output feedback control of polytopic systems using polynomial Lyapunov functions (2010) Proc. 49th IEEE Conf. Decision Control, pp. 6894-6901. , Atlanta, GA, USA, DecemberAgulhari, C.M., Oliveira, R.C.L.F., Peres, P.L.D., LMI relaxations for reduced-order robust Hcontrol of continuous-time uncertain linear systems (2012) IEEE Trans. Autom. Control, 57 (6), pp. 1532-1537. , JuneOliveira, R.C.L.F., Bliman, P.-A., Peres, P.L.D., Robust LMIs with parameters in multi-simplex: Existence of solutions and applications (2008) Proc. 47th IEEE Conf. Decision Control, pp. 2226-2231. , Cancun, Mexico, DecemberYaesh, I., Shaked, U., Robust reduced-order output-feedback Hcontrol (2009) Proc. 6th IFAC Symp. Robust Control Design, pp. 155-160. , Haifa, Israel, JuneEl Ghaoui, L., Oustry, F., Ait-Rami, M., A cone complementarity linearization algorithm for static output feedback and related problems (1997) IEEE Trans. Autom. Control, 42 (8), pp. 1171-1176. , AugustSyrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback-A survey (1997) Automatica, 33 (2), pp. 125-137. , FebruaryChesi, G., Garulli, A., Tesi, A., Vicino, A., Robust stability of timevarying polytopic systems via parameter-dependent homogeneous Lyapunov functions (2007) Automatica, 43 (2), pp. 309-316. , FebruaryDe Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems Perspectives in Robust Control, Ser. Lecture Notes in Control and Information Science, 268, pp. 241-257. , S. O. Reza Moheimani, Ed. New York, NY: Springer-Verlag, 2001Skelton, R.E., Iwasaki, T., Grigoriadis, K., (1998) A Unified Algebraic Approach to Linear Control Design, , Bristol, PA: Taylor & FrancisArzelier, D., Gryazina, E.N., Peaucelle, D., Polyak, B.T., Mixed LMI/Randomized methods for static output feedback control design: Stability and performance (2009) LAAS-CNRS, , Tech. Rep. 09640, SeptemberMoreira, H.R., Oliveira, R.C.L.F., Peres, P.L.D., Robust H2 static output feedback design starting from a parameter-dependent state feedback controller for time-invariant discrete-time polytopic systems (2011) Optim. Control Appl. Meth, 32 (1), pp. 1-13. , January/FebruaryKhalil, H.K., (2002) Nonlinear Systems, , 3rd ed. Upper Saddle River, NJ: Prentice HallBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM Studies in Applied MathematicsOliveira, R.C.L.F., Peres, P.L.D., Parameter-dependent LMIs in robust analysis: Characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations (2007) IEEE Trans. Autom. Control, 52 (7), pp. 1334-1340. , Jul