An eigenvalue based framework is developed for the H-infinity norm analysis and its norm minimization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations (DDAEs). For these equations H-infinity norms are analyzed and their sensitivity with respect to small delay perturbations is studied. Subsequently, numerical methods for the H-infinity norm computation and for designing controllers minimizing the H-infinity norm with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of the approach is illustrated with a software demo. The chapter concludes by pointing out the similarities with the computation and optimization of characteristic roots of DDAEs.
The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that …
In this work, we propose a compositional scheme for the safety controller synthesis of interconnected discrete-time stochastic systems with Markovian switching signals. Our proposed approach is based on a notion of so-called control storage certificates computed for individual subsystems, by leveraging which, one can synthesize state-feedback controllers for interconnected systems to enforce safety specifications over finite time horizons. To do so, we employ a sum-of-squares (SOS) optimization approach to search for multiple storage certificates of each switching subsystem while synthesizing …
The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complex…
In this paper, we focus on mitigating the computational complexity in abstraction-based controller synthesis for interconnected control systems. To do so, we provide a compositional framework for the construction of abstractions for interconnected systems and a bottom-up controller synthesis scheme. In particular, we propose a notion of approximate composition which makes it possible to compute an abstraction of the global interconnected system from the abstractions (possibly of different types) of its components. Finally, by leveraging our notion of approximate composition, we propose a botto…
An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations are analyzed and their stability properties are studied, taking into account the effect of small delay perturbations. Subsequently, numerical methods for stability assessment and for designing stabilizing controllers with a prescribed structure or order, based on a direct optimization approach, are briefly addressed. The effectiveness of the approach is ill…
We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time-delays without any elimination techniques. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs which is robust to arbitrarily small delay perturbations, unlike the standard H-infinity norm. We opt…
In this work, we present a compositional safety controller synthesis approach for the class of discrete-time linear control systems. Here, we leverage a state-of-the-art result on the computation of robust controlled invariant sets. To tackle the complexity of controller synthesis over complex interconnected systems, this paper introduces a decentralized controller synthesis scheme. Rather than treating the interconnected system as a whole, we first design local safety controllers for each subsystem separately to enforce local safety properties, with polytopic state and input constraints as we…
In this paper, we study the stability of suboptimal H-infinity controllers for time-delay systems. The optimal H-infinity controller may have finitely or infinitely many unstable poles. A stable suboptimal H-infinity controller design procedure is given for each of these cases. The design methods are illustrated with examples.
We report on our experience with fixed-order H-infinity controller design using the HIFOO toolbox. We applied HIFOO to various benchmark fixed (or reduced) order H-infinity controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO can be used as an effective alternative to existing methods for fixed-order HIFOO controller design.
This paper proposes a novel method for distributed controller synthesis of homogeneous interconnected systems consisting of identical subsystems. The objective of the designed controller is to minimize the L2-gain of the performance channel. The proposed method is an extended formulation of the Full Block S-Procedure (FBSP) where we introduce an additional set of variables. This allows relaxing the block-diagonal structural assumptions on the Lyapunov and multiplier matrices required for distributed control design, which reduces conservatism w.r.t most existing approaches. We show how to decom…
We report on our experience with strong stabilization using HIFOO, a toolbox for H-infinity fixed-order controller design. We applied HIFOO to 21 fixed-order stable H-infinity controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO often achieves good H-infinity performance with low-order stable controllers, unlike other methods in the literature.
This paper investigates stable suboptimal H-infinity controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the central suboptimal controller) may be unstable with finitely or infinitely many poles in complex right half-plane. For each of these cases search algorithms are proposed to find stable suboptimal H-infinity controllers. These design methods are illustrated with examples.
A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H-infinity controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).
This paper proposes a novel load frequency control (LFC) approach formulated on an optimal structure of the coefficient diagram method (CDM) in a two-area thermal power system. As part of a realistic analysis, nonlinearities related to governor dead band (GDB) and generation rate constraint (GRC) have been considered. In this article, a hybrid CDM method is combined with the optimization of its mathematical equations to achieve an innovative controller. Furthermore, a new metaheuristic optimization technique called the water cycle algorithm (WCA) is used to determine the optimal coefficients o…
The approach in Foias et al. (1996) is one of the well-developed methods to design H-infinity controllers for general infinite dimensional systems. This approach is applicable if the plant admits a special coprime inner/outer factorization. We give the largest class of single-input-single-output (SISO) time delay systems for which this factorization is possible and factorize the admissible plants. Based on this factorization, we compute the optimal H-infinity performance and eliminate unstable pole-zero cancellations in the optimal H-infinity controller. We extend the results on the finite imp…
This article proposes the design of H-infinity-based robust current controller for single-phase grid-feeding voltage source inverter with an LCL filter. The main objective of the proposed controller is to have good reference tracking, disturbance rejection and sufficient LCL resonance damping under a large range of variations of grid impedance. Based on the aforementioned performance requirements, frequency dependent weighting functions are designed. Subsequently, the sub-optimal control problem is formulated and solved to determine the stabilizing controller. Computational footprint of the co…
The skew Toeplitz approach is one of the well developed methods to design H-infinity controllers for infinite dimensional systems. In order to be able to use this method the plant needs to be factorized in some special manner. This paper investigates the largest class of SISO time delay systems for which the special factorizations required by the skew Toeplitz approach can be done. Reliable implementation of the optimal controller is also discussed. It is shown that the finite impulse response (FIR) block structure appears in these controllers not only for plants with I/O delays, but also for …
We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays in the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We presen…
This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing com…
H-infinity controllers are frequently used in control theory due to their robust performance and stabilization. Classical H-infinity controller synthesis methods for finite dimensional LTI MIMO plants result in high-order controllers for high-order plants whereas low-order controllers are desired in practice. We design fixed-order H-infinity controllers for a class of time-delay systems based on a non-smooth, non-convex optimization method and a recently developed numerical method for H-infinity norm computations.
This paper presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the…
We present a new fixed-order H-infinity controller design method for potentially large-scale port-Hamiltonian (pH) plants. Our method computes controllers that are also pH (and thus passive) such that the resulting closed-loop systems is again passive, which ensures closed-loop stability simply from the structure of the plant and controller matrices. In this way, we can avoid computationally expensive eigenvalue computations that would otherwise be necessary. In combination with a sample-based objective function which allows us to avoid multiple evaluations of the H-infinity norm (which is typ…
This paper concentrates on the study of the decentralized fuzzy control method for a class of fractional-order interconnected systems with unknown control directions. To overcome the difficulties caused by the multiple unknown control directions in fractional-order systems, a novel fractional-order Nussbaum function technique is proposed. This technique is much more general than those of existing works since it not only handles single/multiple unknown control directions but is also suitable for fractional/integer-order single/interconnected systems. Based on this technique, a new decentralized…
In this paper we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers, we show that H-infinity controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes. We illustrate connections between the problem solved here and an indirect method for strongly stabilizing H-infinity controller design for systems with time delays.
In this paper, we deal with the power regulation of tethered-wing systems and demonstrate advantages of variable-pitch control in mitigating the dynamic mechanical loads and power fluctuations. The proposed scheme is based on a strategy that maximizes the energy capture during low-speed wind and prevents overloads during the high-speed wind. To realize this strategy, we use a tether reeling-speed controller to track the optimal generator speed during low-speed wind and a MIMO speed-force controller for power limitation during high-speed wind. The controllers are synthesized using H-infinity me…
A classical approach to design controllers for interconnected systems is to assume that the different subsystems operate at different time scales, then design simpler controllers within each time scale, and finally certify stability of the interconnected system via singular perturbation analysis. In this work, we propose an alternative approach that also allows to design the controllers of the individual subsystems separately. However, instead of requiring a sufficiently large time-scale separation, our approach consists of adding a feed-forward term to modify the dynamics of faster systems in…
This manuscript discusses a scalable controller synthesis method for networked systems with a large number of identical subsystems based on the H-infinity control framework. The dynamics of the individual subsystems are described by identical linear time-invariant delay differential equations and the effect of transport and communication delay is explicitly taken into account. The presented method is based on the result that, under a particular assumption on the graph describing the interconnections between the subsystems, the H-infinity norm of the overall system is upper bounded by the robus…
Reliable and secure operation of power systems becomes increasingly challenging as the share of volatile generation rises, leading to largely changing dynamics. Typically, the architecture and structure of controllers in power systems, such as voltage controllers of power generators, are fixed during the design and buildup of the network. As replacing existing controllers is often undesired and challenging, setpoint adjustments, as well as tuning of the controller parameters, are possibilities to counteract large disturbances and changing dynamics. We present an approach for fast and computati…
In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the con…
This paper proposes a new strategy for optimal grid frequency regulation (FR) in an interconnected power system where regional ac grids and an offshore wind farm are linked via a multi-terminal high voltage direct-current (MTDC) network. In the proposed strategy, decentralized H-infinity controllers are developed to coordinate the operations of ac synchronous generators and hybrid MTDC converters, thus achieving optimal power sharing of interconnected ac grids and minimizing frequency deviations in each grid. To develop the controllers, robust optimization problems are formulated and solved us…
We develop a novel decentralized control method for a network of perturbed linear systems with dynamical couplings subject to Signal Temporal Logic (STL) specifications. We first transform the STL requirements into set containment problems and then we develop controllers to solve these problems. Our approach is based on treating the couplings between subsystems as disturbances, which are bounded sets that the subsystems negotiate in the form of parametric assume-guarantee contracts. The set containment requirements and parameterized contracts are added to the subsystems' constraints. We introd…
We consider delay differential algebraic equations (DDAEs) to model interconnected systems with time-delays. The DDAE framework does not require any elimination techniques and can directly deal with any interconnection of systems and controllers with time-delays. In this framework, we analyze the properties of the H-infinity norm of systems described by delay differential algebraic equations. We show that the standard H-infinity norm may be sensitive to arbitrarily small delay perturbations. We introduce the strong H-infinity norm which is insensitive to small delay perturbations and describe …
Robustness and reliability are two key requirements for developing practical quantum control systems. The purpose of this paper is to design a coherent feedback controller for a class of linear quantum systems suffering from Markovian jumping faults so that the closed-loop quantum system has both fault tolerance and H-infinity disturbance attenuation performance. This paper first extends the physical realization conditions from the time-invariant case to the time-varying case for linear stochastic quantum systems. By relating the fault tolerant H-infinity control problem to the dissipation pro…
Weighted sensitivity minimization is studied within the framework of strongly stabilizing (stable) H-infinity controller design for a class of infinite dimensional systems. This problem has been solved by Ganesh and Pearson, [11], for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to a class of unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
This work proposes the adoption of Enhanced Gradient-Based Optimizer (EGBO) as a new approach to the Load Frequency Control (LFC) problem in a two-area interconnected power system. The importance of determining the optimal parameters for the controllers for the LFC problem cannot be overstated, and the fact that estimating these parameters require complex and nonlinear computations makes the optimization procedure even more unique and challenging. Consequently, application of an efficient optimization algorithm to successfully attain optimal controller parameters is critical. To accomplish thi…
In this paper sensitivity minimization problem is considered for a class of unstable time delay systems. Our goal is to find a stable controller stabilizing the feedback system and giving rise to smallest H-infinity norm for the sensitivity function. This problem has been solved by Ganesh and Pearson (1986) for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to include possibly unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.
University of Cambridge（剑桥大学）；CMR Surgical（CMR外科公司）
Most impedance control schemes in robotics implement a desired passive impedance, allowing for stable interaction between the controlled robot and the environment. However, there is little guidance on the selection of the desired impedance. In general, finding the best stiffness and damping parameters is a challenging task. This paper contributes to this problem by connecting impedance control to robust control, with the goal of shaping the robot performances via feedback. We provide a method based on linear matrix inequalities with sparsity constraints to derive impedance controllers that sat…
