Shengxiang Jiang

Distributed control of large segmented telescopes

In this paper we conduct a preliminary study of controlling the primary mirror of a large segmented telescope. This work is motivated by the need of astronomers to study the development of structure in the Universe. First, we present some background about large segmented telescopes and our collaborative research program on large telescopes. Second, we formulate a model of the primary mirror system in state space. Third, we design a centralized controller using H2 methods for a seven-segment system which establishes the best possible performance characteristics for a laboratory-type of unit that we plan to build. Simulation results are displayed. Finally, we apply spatially-invariant distributed control techniques to an infinite segmented system that approximates a large mirror. Through the H2 norm, we calculate upper bounds for the relative displacements between adjacent segments with either a spatially-invariant infinite controller or a truncated local controller. Simulation results are also presented with a truncated local controller applied to a 19-segment system. In all cases, the results indicate that the required accuracy of 10-8 m can be achieved

Performance Optimization of Switched Systems: A Model Matching Approach

In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time-invariant (LTI) systems. The interest is placed on optimizing the worst-case performance of this model matching system over all possible switchings with either l infin-induced norm or H 2 norm as the performance criterion. This optimization is performed over all Youla-Kucera parameters that switch causally in time among n stable LTI systems. For the particular setup at hand, it is shown that the optimal Youla-Kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching, and that it can be obtained as an LTI solution to an associated standard l 1 or H 2 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin-induced and H 2 norm optimizations. An approximate solution with any given precision is possible by finite truncation. Applications of these results to sensitivity minimization, linear switched parameter systems, and cooperative control are provided.

Failure-robust distributed controller architectures

In this paper we consider the problem of designing a controller that is distributed to n processing nodes associated with n collocated control input-measurement output pairs of a given plant. We seek necessary and sufficient conditions so that a controller, distributed in this form, can provide pre-specified performance levels when certain nodes fail. Based on the Youla-Kucera parameterization, the problem can be converted to a convex, structured in Q problem, the solution of which provides a construction for the distributed controller. In addition to nodal failures, we consider the effect of communication noise existing in the transmission of information among nodes, to the regulated variable, and show that this can be precisely captured also in a convex in Q problem.

H2 Control of Large Segmented Telescopes

In this paper we conduct a preliminary study of control of the primary mirror of a large segmented telescope, i.e. aligning the segments to form a paraboloid. This work is motivated by the need of astronomers to study faint objects and to reach the highest possible angular resolution. First, we present background information about large segmented telescopes and our collaborative research program on large telescopes. Second, we formulate a model of the primary mirror system in state space. Third, we design a centralized controller using H2 methods for a seven-segment system which establishes the best possible performance characteristics for the laboratory-type of unit that we plan to build. Simulation results are displayed. Finally, we apply spatially-invariant distributed control techniques to an infinite segmented system that approximates a large mirror. Through the H2 norm, we calculate upper bounds for the relative displacements between adjacent segments with either a spatially-invariant infinite controller or a truncated local controller. Simulation results are also presented with a truncated local controller applied to a 19-segment system. In all cases, the results indicate that the required mirror-to-mirror surface position accuracy of 10-8 m can be achieved.

Design of Distributed Controllers with Constrained and Noisy Links

In this paper we build on our previous work to consider some design aspects of distributed controllers that guarantee a Hinfin performance level. In particular, we consider two design problems. First, is the case where, without loss of generality, there are two distributed subcontrollers connected to a (generalized) plant and the interest is placed in minimizing the number of noise-free (and dynamics free) communication channels between the subcontrollers needed to provide a given performance. The second is the case where, given a distributed controller designed in the first case, communication noise is present and we seek an optimal choice of the communication signals to guarantee a performance level while keeping the communication signal-to-noise power limited. We take an LMI approach to provide solution procedures to these problems and present examples that demonstrate their efficiency

Distributed Controller Design Aspects for Guaranteed Performance

In this paper we consider some design aspects of distributed controllers that guarantee a (H∞or H2) performance level. In particular, we consider two design problems. First is the case where, without loss of generality, there are two distributed subcontollers connected to a (generalized) plant and the interest is placed in minimizing the number of noise-free (and dynamics free) communication channels between the subcontrollers needed to provide a given performance. The second is the case where, given specific signals to be communicated among the subcontrollers, noise is present and we seek to guarantee a performance level while keeping the communication signal to noise power limited. We take an LMI approach to provide solution procedures to these problems and present examples that demonstrate their efficiency.

Switching among structured stabilizing controllers

In this paper we consider the problem of designing a controller K that consists of a set of structured stabilizing components {Km}m n = 1. At each time instant depending on the mode Jm of operation, the corresponding component Km is used. We seek conditions so that a controller, implemented in this form, minimizes the worst case linfin-induced norm under arbitrary switching of the controller among n components, while providing a pre-specified performance level gammam in each operational mode Jm. Based on the Youla-Kucera parameterization, the design problem can be converted into a sequence of linear programming problems, the solutions of which provide an approximate solution of the original problem with any given precision. A numerical example is included to demonstrate the efficiency of algorithms.

On optimal signal reconstruction over switching networks

In this paper we consider signal reconstruction over networks where the communication channel can be modeled as an input switching system (e.g., wireless communication). In particular, we formulate the design problem as a prototypical model matching problem where the various mappings involved belong to a class of input switching systems. The design interest is placed on minimizing the worst case performance of this model matching system over all possible switchings with either l1induced norm or H2 norm as the performance criterion. This minimization is performed over all stable receivers Q in the class of input switching systems. For the particular set-up at hand and in the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in terms of linear programs and quadratic programs respectively for the l1-induced and H2 norm optimizations. An approximate solution with any given precision is possible by finite truncation. Also, it is shown that the optimal receiver Q need not depend on the switching sequence in the cases of partially matched switching and unmatched switching, and that it can be obtained as a linear time-invariant (LTI) solution to an associated l1 induced or H2 norm optimization.

On l∞ performance optimization of switched systems

In this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n given linear time invariant (LTI) systems. The interest is placed on minimizing the worst case lscrinfin-induced norm of this model matching system over all possible switchings. This minimization is performed over all Youla-Kucera parameters Q that switch causally in time over n (stable) LTI systems. For the particular set-up at hand, it is shown that the optimal Youla-Kucera parameter Q need not depend on the switching sequence in the case of partially matched switching, and that it can be obtained as an LTI solution to an associated standard lscr1 optimization. In the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in linear programming, and an approximate solution with any given precision is possible by finite truncation.

Distributed Control over Structured and Lossy Networks

In this paper we consider distributed control of n dynamic agents to optimize an overall system performance metric. Due to limited communication resources, there exist structured interconnections among the agents and the design interest is placed in synthesizing a suitably distributed control law to provide a given performance level. Based on a Youla-Kucera parameterization approach, the problem of designing a distributed controller to deliver given performance levels for different network topologies is convex in the Youla-Kucera parameter Q. Furthermore, if packet drops exist in information transmission among the agents, we provide convex conditions to guarantee mean square stability and optimize system performance.