New delay-dependent stability criteria for recurrent neural networks with time-varying delays

Dimirovski, Georgi M. (Dogus Author)This work is concerned with the delay-dependentstability problem for recurrent neural networks with time-varying delays. A new improved delay-dependent stability criterion expressed in terms of linear matrix inequalities is derived by constructing a dedicated Lyapunov-Krasovskii functional via utilizing Wirtinger inequality and convex combination approach. Moreover, a further improved delay-dependent stability criterion is established by means of a new partitioning method for bounding conditions on the activation function and certain new activation function conditions presented. Finally, the application of these novel results to an illustrative example from the literature has been investigated and their effectiveness is shown via comparison with the existing recent ones

Fuzzy control turns 50: 10 years later

In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.Guerra, T.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later. Fuzzy Sets and Systems. 281:162-182. doi:10.1016/j.fss.2015.05.005S16218228

Analysis of input delay systems using integral quadratic constraint

The L2-gain computation of a linear time-invariant system with state and input delay is discussed. The input and the state delay are handled separately by using dissipation inequality involving a Lyapunov-Krasovskii functional and integral quadratic constraints. A conic combination of IQCs is proposed for characterizing the input delay, where the coefficients are linear time-invariant systems. The numerical example (a vehicle platoon) confirm that using this dissipativity approach a more effective method for L2-gain computation is obtained

Stability analysis and control of discrete-time systems with delay

The research presented in this thesis considers the stability analysis and control of discrete-time systems with delay. The interest in this class of systems has been motivated traditionally by sampled-data systems in which a process is sampled periodically and then controlled via a computer. This setting leads to relatively cheap control solutions, but requires the discretization of signals which typically introduces time delays. Therefore, controller design for sampled-data systems is often based on a model consisting of a discrete-time system with delay. More recently the interest in discrete-time systems with delay has been motivated by networked control systems in which the connection between the process and the controller is made through a shared communication network. This communication network increases the flexibility of the control architecture but also introduces effects such as packet dropouts, uncertain time-varying delays and timing jitter. To take those effects into account, typically a discrete-time system with delay is formulated that represents the process together with the communication network, this model is then used for controller design While most researchers that work on sampled-data and networked control systems make use of discrete-time systems with delay as a modeling class, they merely use these models as a tool to analyse the properties of their original control problem. Unfortunately, a relatively small amount of research on discrete-time systems with delay addresses fundamental questions such as: What trade-off between computational complexity and conceptual generality or potential control performance is provided by the different stability analysis methods that underlie existing results? Are there other stability analysis methods possible that provide a better trade-off between these properties? In this thesis we try to address these and other related questions. Motivated by the fact that almost every system in practice is subject to constraints and Lyapunov theory is one of the few methods that can be easily adapted to deal with constraints, all results in this thesis are based on Lyapunov theory. In Chapter 2 we introduce delay difference inclusions (DDIs) as a modeling class for systems with delay and discuss their generality and advantages. Furthermore, the two standard stability analysis results for DDIs that make use of Lyapunov theory, i.e., the Krasovskii and Razumikhin approaches, are considered. The Krasovskii approach provides necessary and sufficient conditions for stability while the Razumikhin approach provides conditions that are relatively simple to verify but conservative. An important conclusion is that the Razumikhin approach makes use of conditions that involve the system state only while those corresponding to the Krasovskii approach involve trajectory segments. Therefore, only the Razumikhin approach yields information about DDI trajectories directly, such that the corresponding computations can be executed in the low-dimensional state space of the DDI dynamics. Hence, we focus on the Razumikhin approach in the remainder of the thesis. In Chapter 3 it is shown that by considering each delayed state as a subsystem, the behavior of a DDI can be described by an interconnected system. Thus, the Razumikhin approach is found to be an exact application of the small-gain theorem, which provides an explanation for the conservatism that is typically associated with this approach. Then, inspired by the relation of DDIs to interconnected systems, we propose a new Razumikhin-type stability analysis method that makes use of a stability analysis result for interconnected systems with dissipative subsystems. The proposed method is shown to provide a trade-off between the conceptual generality of the Krasovskii approach and the computationally convenience of the Razumikhin approach. Unfortunately, these novel Razumikhin-type stability analysis conditions still remain conservative. Therefore, in Chapter 4 we propose a relaxation of the Razumikhin approach that provides necessary and sufficient conditions for stability. Thus, we obtain a Razumikhin-type result that makes use of conditions that involve the system state only and are non-conservative. Interestingly, we prove that for positive linear systems these conditions equivalent to the standard Razumikhin approach and hence both are necessary and sufficient for stability. This establishes the dominance of the standard Razumikhin approach over the Krasovskii approach for positive linear discrete-time systems with delay. Next, in Chapter 5 the stability analysis of constrained DDIs is considered. To this end, we study the construction of invariant sets. In this context the Krasovskii approach leads to algorithms that are not computationally tractable while the Razumikhin approach is, due to its conservatism, not always able to provide a suitable invariant set. Based on the non-conservative Razumikhin-type conditions that were proposed in Chapter 4, a novel invariance notion is proposed. This notion, called the invariant family of sets, preserves the conceptual generality of the Krasovskii approach while, at the same time, it has a computational complexity comparable to the Razumikhin approach. The properties of invariant families of sets are analyzed and synthesis methods are presented. Then, in Chapter 6 the stabilization of constrained linear DDIs is considered. In particular, we propose two advanced control schemes that make use of online optimization. The first scheme is designed specifically to handle constraints in a non-conservative way and is based on the Razumikhin approach. The second control scheme reduces the computational complexity that is typically associated with the stabilization of constrained DDIs and is based on a set of necessary and sufficient Razumikhin-type conditions for stability. In Chapter 7 interconnected systems with delay are considered. In particular, the standard stability analysis results based on the Krasovskii as well as the Razumikhin approach are extended to interconnected systems with delay using small-gain arguments. This leads, among others, to the insight that delays on the channels that connect the various subsystems can not cause the instability of the overall interconnected system with delay if a small-gain condition holds. This result stands in sharp contrast with the typical destabilizing effect that time delays have. The aforementioned results are used to analyse the stability of a classical power systems example where the power plants are controlled only locally via a communication network, which gives rise to local delays in the power plants. A reflection on the work that has been presented in this thesis and a set of conclusions and recommendations for future work are presented in Chapter 8

Robust Delay-Dependent Load Frequency Control of Wind Power System Based on a Novel Reconstructed Model

IEEE This article presents a novel reconstructed model for the delayed load frequency control (LFC) schemes considering wind power, which aims to improve the computational efficiency for PID controllers while retaining their dynamic performance. Via fully exploiting system states influenced by time delays directly, this novel reconstructed method is proposed with a controller isolated. Hence, when the PID controllers are unknown, the stability criterion based on this model can resolve controller gains with less time consumed. For given PID gains, this model can be employed to establish criteria for stability analysis, which can realize the tradeoff between the calculation accuracy and efficiency. The case study is first based on a two-area traditional LFC system to validate the merits of a novel reconstructed model, including accurately estimating the influence of time delay on system frequency stability with increased computational capability. Then, under traditional and deregulated environments, case studies are carried out on the two-area and three-area schemes, respectively. Through the novel reconstructed model, the efficiency of obtaining controller parameters is highly improved while their robustness against the random wind power, tie-line power changes, inertial reductions, and time delays remains almost unchanged

Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer

[EN] The problem of output stabilization and disturbance rejection for input-delayed systems is tackled in this work. First, a suitable transformation is introduced to translate mismatched disturbances into an equivalent input disturbance. Then, an extended state observer is combined with a predictive observer structure to obtain a future estimation of both the state and the disturbance. A disturbance model is assumed to be known but attenuation of unmodeled components is also considered. The stabilization is proved via Lyapunov-Krasovskii functionals, leading to sufficient conditions in terms of linear matrix inequalities for the closed-loop analysis and parameter tuning. The proposed strategy is illustrated through a numerical example.PROMETEOII/2013/004; Conselleria d'Educacio; Generalitat Valenciana, Grant/Award Number: TIN2014-56158-C4-4-P-AR; Ministerio de Economia y Competitividad, Grant/Award Number: FPI-UPV 2014; Universitat Politecnica de ValenciaSanz Diaz, R.; García Gil, PJ.; Fridman, E.; Albertos Pérez, P. (2018). Rejection of mismatched disturbances for systems with input delay via a predictive extended state observer. International Journal of Robust and Nonlinear Control. 28(6):2457-2467. https://doi.org/10.1002/rnc.4027S24572467286Stability and Stabilization of Systems with Time Delay. (2011). IEEE Control Systems, 31(1), 38-65. doi:10.1109/mcs.2010.939135Fridman, E. (2014). Introduction to Time-Delay Systems. Systems & Control: Foundations & Applications. doi:10.1007/978-3-319-09393-2Watanabe, K., & Ito, M. (1981). A process-model control for linear systems with delay. IEEE Transactions on Automatic Control, 26(6), 1261-1269. doi:10.1109/tac.1981.1102802Astrom, K. J., Hang, C. C., & Lim, B. C. (1994). A new Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, 39(2), 343-345. doi:10.1109/9.272329Matausek, M. R., & Micic, A. D. (1996). A modified Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, 41(8), 1199-1203. doi:10.1109/9.533684García, P., & Albertos, P. (2008). A new dead-time compensator to control stable and integrating processes with long dead-time. Automatica, 44(4), 1062-1071. doi:10.1016/j.automatica.2007.08.022Normey-Rico, J. E., & Camacho, E. F. (2009). Unified approach for robust dead-time compensator design. Journal of Process Control, 19(1), 38-47. doi:10.1016/j.jprocont.2008.02.003Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Artstein, Z. (1982). Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control, 27(4), 869-879. doi:10.1109/tac.1982.1103023Krstic, M. (2008). Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch. Automatica, 44(11), 2930-2935. doi:10.1016/j.automatica.2008.04.010Léchappé, V., Moulay, E., Plestan, F., Glumineau, A., & Chriette, A. (2015). New predictive scheme for the control of LTI systems with input delay and unknown disturbances. Automatica, 52, 179-184. doi:10.1016/j.automatica.2014.11.003Sanz, R., Garcia, P., & Albertos, P. (2016). Enhanced disturbance rejection for a predictor-based control of LTI systems with input delay. Automatica, 72, 205-208. doi:10.1016/j.automatica.2016.05.019Basturk, H. I., & Krstic, M. (2015). Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay. Automatica, 58, 131-138. doi:10.1016/j.automatica.2015.05.013Basturk, H. I. (2017). Cancellation of unmatched biased sinusoidal disturbances for unknown LTI systems in the presence of state delay. Automatica, 76, 169-176. doi:10.1016/j.automatica.2016.10.006Sanz, R., Garcia, P., Albertos, P., & Zhong, Q.-C. (2016). Robust controller design for input-delayed systems using predictive feedback and an uncertainty estimator. International Journal of Robust and Nonlinear Control, 27(10), 1826-1840. doi:10.1002/rnc.3639Mondie, S., & Michiels, W. (2003). Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Transactions on Automatic Control, 48(12), 2207-2212. doi:10.1109/tac.2003.820147Zhong, Q.-C. (2004). On Distributed Delay in Linear Control Laws—Part I: Discrete-Delay Implementations. IEEE Transactions on Automatic Control, 49(11), 2074-2080. doi:10.1109/tac.2004.837531Zhou, B., Lin, Z., & Duan, G.-R. (2012). Truncated predictor feedback for linear systems with long time-varying input delays. Automatica, 48(10), 2387-2399. doi:10.1016/j.automatica.2012.06.032Zhou, B., Li, Z.-Y., & Lin, Z. (2013). On higher-order truncated predictor feedback for linear systems with input delay. International Journal of Robust and Nonlinear Control, 24(17), 2609-2627. doi:10.1002/rnc.3012Besançon G Georges D Benayache Z Asymptotic state prediction for continuous-time systems with delayed input and application to control IEEE 2007 Kos, GreeceNajafi, M., Hosseinnia, S., Sheikholeslam, F., & Karimadini, M. (2013). Closed-loop control of dead time systems via sequential sub-predictors. International Journal of Control, 86(4), 599-609. doi:10.1080/00207179.2012.751627Léchappé V Moulay E Plestan F Dynamic observation-prediction for LTI systems with a time-varying delay in the input IEEE 2016 Las Vegas, NVCacace, F., Conte, F., Germani, A., & Pepe, P. (2016). Stabilization of strict-feedback nonlinear systems with input delay using closed-loop predictors. International Journal of Robust and Nonlinear Control, 26(16), 3524-3540. doi:10.1002/rnc.3517Mazenc, F., & Malisoff, M. (2017). Stabilization of Nonlinear Time-Varying Systems Through a New Prediction Based Approach. IEEE Transactions on Automatic Control, 62(6), 2908-2915. doi:10.1109/tac.2016.2600500Guo, L., & Chen, W.-H. (2005). Disturbance attenuation and rejection for systems with nonlinearity via DOBC approach. International Journal of Robust and Nonlinear Control, 15(3), 109-125. doi:10.1002/rnc.978Fridman, E. (2003). Output regulation of nonlinear systems with delay. Systems & Control Letters, 50(2), 81-93. doi:10.1016/s0167-6911(03)00131-2Isidori, A., & Byrnes, C. I. (1990). Output regulation of nonlinear systems. IEEE Transactions on Automatic Control, 35(2), 131-140. doi:10.1109/9.45168Ding, Z. (2003). 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Sampled-data Networked Control Systems: A Lyapunov-Krasovskii Approach

The main goal of this thesis is to develop computationally efficient methods for stability analysis and controller synthesis of sampled-data networked control systems. In sampled-data networked control systems, the sensory information and feedback signals are exchanged among different components of the system (sensors, actuators, and controllers) through a communication network. Stabilization of sampled-data networked control systems is a challenging problem since the introduction of multirate sample and holds, time-delays, and packet losses into the system degrades its performance and can lead to instability. A diverse range of systems with linear, piecewise affine (PWA), and nonlinear vector fields are studied in this thesis. PWA systems are a class of state-based switched systems with affine vector field in each mode. Stabilization of PWA networked control systems are even more challenging since they simultaneously involve switches due to the hybrid vector fields (state-based switching) and switches due to the sample and hold devices in the network (event-based switching). The objectives of this thesis are: (a) to design controllers that guarantee exponential stability of the system for a desired sampling period; (b) to design observers that guarantee exponential convergence of the estimation error to the origin for a desired sampling period; and (c) given a controller, to find the maximum allowable network-induced delay that guarantees exponential stability of the sampled-data networked control system. Lyapunov-Krasovskii based approaches are used to propose sufficient stability and stabilization conditions for sampled-data networked control systems. Convex relaxation techniques are employed to cast the proposed stability analysis and controller synthesis criteria in terms of linear matrix inequalities that can be solved efficiently