6,507 research outputs found
Fixed zeros of decentralized control systems
This paper considers the notion of decentralized fixed zeros for linear, time-invariant, finite-dimensional systems. For an N-channel plant that is free of unstable decentralized fixed modes, an unstable decentralized fixed zero of Channel i (1 ≤ i ≤ N) is defined as an element of the closed right half-plane, which remains as a blocking zero of that channel under the application of every set of N - 1 controllers around the other channels, which make the resulting single-channel system stabilizable and detectable. This paper gives a complete characterization of unstable decentralized fixed zeros in terms of system-invariant zeros
Time Complexity of Decentralized Fixed-Mode Verification
Given an interconnected system, this note is concerned with the time complexity of verifying whether an unrepeated mode of the system is a decentralized fixed mode (DFM). It is shown that checking the decentralized fixedness of any distinct mode is tantamount to testing the strong connectivity of a digraph formed based on the system. It is subsequently proved that the time complexity of this decision problem using the proposed approach is the same as the complexity of matrix multiplication. This work concludes that the identification of distinct DFMs (by means of a deterministic algorithm, rather than a randomized one) is computationally very easy, although the existing algorithms for solving this problem would wrongly imply that it is cumbersome. This note provides not only a complexity analysis, but also an efficient algorithm for tackling the underlying problem
Static Output Feedback: On Essential Feasible Information Patterns
In this paper, for linear time-invariant plants, where a collection of
possible inputs and outputs are known a priori, we address the problem of
determining the communication between outputs and inputs, i.e., information
patterns, such that desired control objectives of the closed-loop system (for
instance, stabilizability) through static output feedback may be ensured.
We address this problem in the structural system theoretic context. To this
end, given a specified structural pattern (locations of zeros/non-zeros) of the
plant matrices, we introduce the concept of essential information patterns,
i.e., communication patterns between outputs and inputs that satisfy the
following conditions: (i) ensure arbitrary spectrum assignment of the
closed-loop system, using static output feedback constrained to the information
pattern, for almost all possible plant instances with the specified structural
pattern; and (ii) any communication failure precludes the resulting information
pattern from attaining the pole placement objective in (i).
Subsequently, we study the problem of determining essential information
patterns. First, we provide several necessary and sufficient conditions to
verify whether a specified information pattern is essential or not. Further, we
show that such conditions can be verified by resorting to algorithms with
polynomial complexity (in the dimensions of the state, input and output).
Although such verification can be performed efficiently, it is shown that the
problem of determining essential information patterns is in general NP-hard.
The main results of the paper are illustrated through examples
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Improved branch and bound method for control structure screening
The main aim of this paper is to present an improved algorithm of “Branch and
Bound” method for control structure screening. The new algorithm uses a best-
first search approach, which is more efficient than other algorithms based on
depth-first search approaches. Detailed explanation of the algorithms is
provided in this paper along with a case study on Tennessee–Eastman process to
justify the theory of branch and bound method. The case study uses the Hankel
singular value to screen control structure for stabilization. The branch and
bound method provides a global ranking to all possible input and output
combinations. Based on this ranking an efficient control structure with least
complexity for stabilizing control is detected which leads to a decentralized
proportional cont
A new momentum management controller for the space station
A new approach to CMG (control moment gyro) momentum management and attitude control of the Space Station is developed. The control algorithm utilizes both the gravity-gradient and gyroscopic torques to seek torque equilibrium attitude in the presence of secular and cyclic disturbances. Depending upon mission requirements, either pitch attitude or pitch-axis CMG momentum can be held constant: yaw attitude and roll-axis CMG momentum can be held constant, while roll attitude and yaw-axis CMG momentum cannot be held constant. As a result, the overall attitude and CMG momentum oscillations caused by cyclic aero-dynamic disturbances are minimized. A state feedback controller with minimal computer storage requirement for gain scheduling is also developed. The overall closed-loop system is stable for + or - 30 percent inertia matrix variations and has more than + or - 10 dB and 45 deg stability margins in each loop
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