This paper is concerned with the filter design problem for linear parameter varying (LPV) discrete-time systems with nonlinearities described by integral quadratic constraints. The LPV system is considered to have an ...
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ISBN:
(纸本)9781509007592
This paper is concerned with the filter design problem for linear parameter varying (LPV) discrete-time systems with nonlinearities described by integral quadratic constraints. The LPV system is considered to have an arbitrary dependence on the time-varying parameters, not necessarily rational. The filter designed assures a bound to the worst case gain from the disturbance input to the filtering error. The development of the proposed approach is based on the existence of a quadratic storage function. The conditions are given in terms of linear matrix inequalities and are derived through congruence transformations and change of variables. Numerical examples illustrate the applicability and performance of the proposed method.
A number of Linear Matrix Inequality (LMI) conditions for the design of gain-scheduled quadratic H-infinity output-feedback controllers can be found in the literature under a variety of assumptions on both the system ...
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ISBN:
(纸本)9781509007592
A number of Linear Matrix Inequality (LMI) conditions for the design of gain-scheduled quadratic H-infinity output-feedback controllers can be found in the literature under a variety of assumptions on both the system as well as the controller structure. The first contribution of the present paper is to provide a catalog of such conditions, including some new conditions, which cover most practical applications. In each setup, LMI conditions allowing implicit and explicit computation of the controller matrices are provided. As a second contribution, we illustrate how to use these conditions and compare their performance using a numerical example which allows us to exercise the controller design procedure in the various scenarios covered.
This paper addresses the design problem of feedforward controllers for discrete-time Linear Time-Invariant (LTI) plant systems under the condition that prior external signals (e.g. disturbance or reference input) are ...
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ISBN:
(纸本)9781509007592
This paper addresses the design problem of feedforward controllers for discrete-time Linear Time-Invariant (LTI) plant systems under the condition that prior external signals (e.g. disturbance or reference input) are measurable online and can be exploited as the input to the feedforward controllers. The representation of descriptor systems is adopted to incorporate the prior external signals into the LTI plant systems. We propose a design method for our problem via the dual formulation of Generalized KYP (GKYP) lemma by considering that GKYP lemma can reduce the numerical complexity in controller design, because it has an ability to specify the frequency ranges of control requirements without introducing weighting functions. We extend the method to the case that plant systems have uncertainties represented as polytopic systems. Academic examples show the usefulness of our proposed methods.
This paper proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered ...
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ISBN:
(纸本)9781509007592
This paper proposes an algorithmic approach to synthesize stabilizing control laws for discrete-time piecewise affine probabilistic (PWAP) systems based on computations of probabilistic reachable sets. The considered class of systems contains probabilistic components (with Gaussian distribution) modeling additive disturbances and state initialization. The probabilistic reachable state sets contain all states that are reachable with a given confidence level under the effect of time-variant control laws. The control synthesis uses principles of the ellipsoidal calculus, and it considers that the system parametrization depends on the partition of the state space. The proposed algorithm uses LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints and transitions between regions of the state space are considered. The formulation of the SDP is adopted from a previous work in [1] for switched systems, in which the switching of the continuous dynamics is triggered by a discrete input variable. Here, as opposed to [1], the switching occurs autonomously and an algorithmic procedure is suggested to synthesis a stabilizing controller. An example for illustration is included.
This paper considers the synthesis of distributed reactive control protocols for a Boolean network in a distributed manner. We start with a directed acyclic graph representing a network of Boolean subsystems and a glo...
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ISBN:
(纸本)9781509007592
This paper considers the synthesis of distributed reactive control protocols for a Boolean network in a distributed manner. We start with a directed acyclic graph representing a network of Boolean subsystems and a global contract, given as an assumption-guarantee pair. Assumption captures the environment behavior, and guarantee is the requirements to be satisfied by the system. Local assumption-guarantee contracts, together with local control protocols ensuring these local contracts, are computed recursively for each subsystem based on the partial order structure induced by the directed acyclic graph. By construction, implementing these local control protocols together guarantees the satisfaction of the global assumption-guarantee contract. Moreover, local control protocol synthesis reduces to quantified satisfiability (QSAT) problems in this setting. We also discuss structural properties of the network that affect the completeness of the proposed algorithm. As an application, we show how an aircraft electric power system can be represented as a Boolean network, and we synthesize distributed control protocols from a global assumption-guarantee contract. The assumptions capture possible failures of the system components, and the guarantees capture safety requirements related to power distribution.
The design of explicit constrained control is relatively simple when a controlled contractive set is available. However, the complexity of the explicit controller will depend on the complexity of the controlled contra...
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ISBN:
(纸本)9781509007592
The design of explicit constrained control is relatively simple when a controlled contractive set is available. However, the complexity of the explicit controller will depend on the complexity of the controlled contractive set. The ability to design a low complexity controlled contractive set is therefore desirable. Most methods for finding controlled contractive sets either assume the use of a constant linear state feedback, or exploit reachable set computations. In the first case, the assumption of a constant linear state feedback is restrictive (as controllers for constrained linear systems, such as MPC, are typically piecewise affine), while in the second case the complexity of the controlled contractive set may be very high. Initial results on the construction of low complexity controlled contractive sets without assuming linear state feedback were reported in the recent literature. The present paper extends these results, including the ability to handle more general classes of system dynamics. The paper develops a method for finding a controlled contractive set of a specified complexity, allowing for a trade-off between the complexity of the set and its volume.
The design of full-order state observers with error limitation can be performed by using set invariance concepts, together with the multiparametric programming technique, which presents, as solution, piecewise affine ...
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ISBN:
(纸本)9781509007592
The design of full-order state observers with error limitation can be performed by using set invariance concepts, together with the multiparametric programming technique, which presents, as solution, piecewise affine (PWA) output injection laws over polyhedral regions. However, this technique has some disadvantages when applied to multiple-output systems, such as complex calculations, high computational cost, and considerable memory requirements. In order to reduce the computational complexity of the offline solution in multiple-output systems, this paper shows how the K q-flat data cluster analysis algorithm can be used to establish a smaller number of polyhedral regions which are able to confine the estimation error in a constraints set. Optimization problems are also formulated in order to significantly reduce the number of regions, but resulting in suboptimal observers. Finally, a comparison between the proposed approach and the multiparametric programming technique is presented through a numerical example which shows how the complexity of the set-invariant observers can be reduced by our technique.
In this paper we present a method to simultaneously design a static state feedback gain and the trigger function to stabilize discrete-time LTI systems subject to actuator saturation under an event-triggered strategy....
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This paper is concerned with the problem of H-2 dynamic output feedback control for discrete-time Markov jump linear systems (MJLS) whose transition probability matrix is affected by uncertainties. A two step procedur...
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ISBN:
(纸本)9781509007592
This paper is concerned with the problem of H-2 dynamic output feedback control for discrete-time Markov jump linear systems (MJLS) whose transition probability matrix is affected by uncertainties. A two step procedure based on linear matrix inequality (LMI) conditions is used to solve the problem. In the first step, a stabilizing parameter-dependent state feedback gain is computed. The gain, not implementable, is used as an input in the second step, where sufficient LMI conditions provide an H-2 guaranteed cost dynamic output feedback controller for the MJLS. Reduced order and mode-independent controllers can be readily obtained from the conditions, due to the fact that the matrices of the controller realization are constructed only in terms of decision variables. As illustrated by an example, less conservative controllers with more accurate estimates of the H-2 norm bound can be obtained through the proposed methodology. Moreover, lower H-2 bounds can be guaranteed at the price of searching for a scalar parameter and increasing the degrees of the polynomial decision variables involved in the optimization process.
Hardware-in-the-Loop (HIL) and Rapid control Prototyping (RPC) are extensively used techniques for the design of controlsystems. Matlab-based commercial tools for HIL and RPC usually are not cost-effective for most u...
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