Martin Papík

Decentralized control and communication

Abstract In this paper, the past and current issues involved in the design of decentralized networked control systems are reviewed. The basic models of interconnected systems described as continuous-time linear time-invariant systems in the time domain serve as a framework for the inclusion of communication channels in the decentralized feedback loop. The I/O-oriented models and the interaction oriented models with disjoint subsystems and interactions are distinguished. The overview is focused on packet dropouts, transmission delays, and quantization effects which are included in the time-driven design of feedback loop components. Single- and multiple-packet transmissions are considered in this contents. The design of decentralized state feedback gain matrices with delayed feedback uses the methodology of sampled-data feedback design for continuous-time systems, while the decentralized H ∞ quantizer design is based on the static output controller. The Liapunov stability approach results in computationally efficient decentralized control design strategies described by using linear matrix inequalities.

Decentralized Networked Control of Building Structures

The article presents a new method for the design of decentralized networked switched controllers to mitigate the response of building structures under earthquakes. It consists of two phases. The first phase generates low-order gain matrices based on the linear quadratic Gaussian LQG control design. It includes a substructural approach when the equations of motion of substructures are extracted from the equation of motion of the overall structures described by a finite element in-plane 2-D model. Appropriate model reduction procedures, determination of damping as well as the selection of sensor and actuators locations and models are applied to each substructure. The sensors and actuators are implemented into the design model. Both resulting reduced-order state space models of substructures are used for the proper LQG control design. The obtained local controllers are implemented into the overall structure to evaluate the performance of the closed-loop system. Displacement, drift, acceleration, maximal actuator forces as well as dynamic responses on selected locations are checked. The computational originality is the method derived under the subsequent second phase, where the gain matrices computed in the first phase serve as a tool for the design of decentralized networked switched controller. The switching is realized periodically between two switched modes. Each mode corresponds with only one active local feedback loop for a certain period of time. The network parameter is the time interval of activity of each mode determined by a given protocol. Robustness of performance against packet dropouts and sensor faults is tested. A numerical example of the decentralized networked switched controller design applied on the 20-story high-fidelity building benchmark model is supplied. The simulation tests show the proposed method exhibits acceptable performance.

Decentralized H -infinity control of complex systems with delayed feedback

The paper studies the problem of decentralized H ∞ fault tolerant state feedback control design for a class of continuous-time complex systems composed of identical subsystems and symmetric interconnections. We consider a time-varying interval-bounded delay in the feedback of each channel. Single delay as well as multiple delay cases is considered. By exploiting a particular structure of the systems, sufficient conditions are derived for the gain matrix selection. The controller design is performed using a reduced-order system under linear matrix inequality approach constraints. The asymptotic stability with disturbance attenuation γ of the overall multiple delay closed-loop system is guaranteed when synthesizing the gain matrix into the decentralized controller. Moreover, sufficient conditions for the H ∞ bound tolerance under local control channel failures of the overall closed-loop system are derived. The tolerance can be easily tested on several low-order systems. A numerical example illustrates the effectiveness of the proposed method.

Decentralized stabilization of complex systems with delayed feedback

Abstract The paper studies the problem of decentralized state feedback control design for a class of continuous-time complex systems. These systems are composed of identical nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations. We consider local time-varying delayed feedback at each channel. Single delay as well as multiple delay cases are considered. By exploiting the special structure of the systems, sufficient conditions are derived for the gain matrix selection performed on the design system of reduced dimension under linear matrix inequality approach constraints. It is shown that the robust delay-dependent stability of the global multiple delay closed-loop system is guaranteed when implementing the gain matrix into the global decentralized controller. Moreover, sufficient conditions are derived for the tolerance of local control channel failures in such a global closed-loop system. The fault tolerance can be effectively tested on systems of reduced dimensions.

Decentralized stabilization of symmetric systems with delayed observer-based feedback

This paper examines decentralized observer-based stabilization for symmetric interconnected systems. The structure of these systems is composed of identical subsystems with symmetric interconnections. Linear time-invariant dynamic systems are considered within the continuous-time case. The observer inputs operate with a delayed system output. Single as well as multiple time-varying interval bounded delays in the loop are considered. The state space matrices of these systems are decomposable into block diagonal matrices. Their properties and a robust stabilization approach are used to construct the design model which is subsequently used for the gain matrices selection by using Linear Matrix Inequalities. The main result shows that when these gain matrices are implemented into the overall system as local controller-observers, then the entire closed-loop system guarantees asymptotic stability. An application example illustrates the effectiveness of this method.

Decentralized stabilization of large-scale civil structures

Abstract The objective of this investigation is to present a decentralized design of decentralized controllers for a 20-story steel structure benchmark. The benchmark problem was proposed within the structural control community to design and compare control schemes for seismically excited buildings. The control design problem is focused on an in-plane analysis of one-half of the structure. The height of the building naturally suggests the disjoint decomposition of a finite element overall dynamic model into two subsystems, each covering 10 stories. Inter-story elements appearing between the 10th and the 11th fool serve as the coupling elements of the overall interconnected system. The idea of decentralization of control has been numerically tested and compared to the benchmark sample centralized LQG design. The performance of the decentralized control design has been assessed by means of given benchmark evaluation criteria, eigenvalue analysis and time responses for both pre-earthquake and post-earthquake structures.

Stabilization of decentralized networked complex systems with multiple-packet transmission

The paper presents the decentralized control design for a class of networked continuous-time complex systems by using the multiple-packet transmission approach. Such a class is composed of identical nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations. The system structure enables the model reduction and the subsequent usage of a single-packet transmission approach to select the robustly delay-dependent stabilizing gain matrix for the reduced model. The inclusion of the effect of data-packet dropout and communication delays in the feedback loop is enabled by using the linear matrix inequality approach. It is shown how such a gain matrix when implemented as local controllers in the local networked channel loops leads to a robustly delay-dependent stable overall closed-loop system with multiple delays. The simulation results illustrate the effectiveness of the proposed methodology.

Quantized event-triggered static output feedback stabilization

The article presents new sufficient conditions for the stabilization of decentralized model-based event-triggered control systems with quantized static output feedback. Relative threshold strategies with logarithmic quantizers are developed for unstructured, I/O-structured and interaction-structured uncertain nominally linear dynamical systems. A disjoint subsystem-interconnection structure is analyzed for interaction-structured plants. The error thresholds are designed in a decentralized manner for structured systems, when only local information about the system is available. A numerical illustrative example of quantized coupled subsystems with uncertainties in all system matrices is supplied to render the effectiveness of the proposed method.

Decentralized Stabilization of Discrete-Time Networked Strongly Coupled Complex Systems

Abstract In this paper, the authors present an approach to decentralized stabilization with delayed feedback for a class of networked discrete-time complex systems. A class of dynamic discrete-time systems with identical linear nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations is considered. The proposed method is based on particular structural properties of these systems which enable to construct a reduced order control design model with equivalent dynamic properties as the original system. Then, the standard method of linear matrix inequalities is used to design the gain matrix for such reduced model. The effect of data-packet dropout and communication delays between the plant and the controller is included in the controller design. It is shown how this methodology can simplify the control design with time-varying delay in the input. For such a purpose, a delay-dependent approach is applied in order to obtain a robustly delay-dependent stable overall closed-loop system with a decentralized controller.