On the solvability of the constrained Lyapunov problem

Journal ArticleThis paper considers system theoretic conditions for the solvability of the so-called constrained Lyapunov problem for nonsquare systems. These problems commonly appear in the control systems literature. Both a static output feedback problem and an observer problem are considered. The basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way. © 2007 IEEE

Distributed model predictive control for the atmospheric and vacuum distillation towers in a petroleum refining process

This paper develops a distributed model predictive control strategy for the atmospheric and vacuum distillation tower, which constitutes a key process involved in refining petroleum. When considering an MPC implementation, it is known that computational complexity can be reduced if the system is first decomposed into multiple smaller dimensional subsystems. Optimally exploiting the modern computer networks available in industry, a distributed model predictive control implementation is developed for the atmospheric and vacuum tower system, which is assumed to be part of a wider petroleum refining process comprised of a number of sub-systems connected in series. For each subsystem, given the availability of mutual communication channels between subsystems and by using an iterative calculation approach, it will be seen that Nash optimality can be achieved. A low-cost solution that is readily implementable online is seen to achieve the control objective. The effectiveness of the approach presented in the paper is validated by the results of nonlinear simulation experiments

Dynamic output feedback sliding mode control for uncertain linear systems

In this paper, a class of uncertain linear systems with unmatched disturbances is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is designed which is dependent on the system output, observed state, and estimated uncertain parameters. A linear coordinate transformation is introduced so that the stability analysis of the reduced-order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the considered system state to reach the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example for a high incidence research model (HIRM) aircraft is used to demonstrate the effectiveness of the proposed method

Dynamic output feedback sliding mode control for non-minimum phase systems with application to an inverted pendulum

In this paper, a class of nonlinear systems is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is proposed which is a function of the measured system output and an estimated state. A linear coordinate transformation is introduced so that the stability analysis of the reduced order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example is used to demonstrate the effectiveness of the proposed method and the method is successfully applied to an inverted pendulum

Consensus Control for a Class of Linear Multiagent Systems using a Distributed Integral Sliding Mode Strategy

In this paper, a consensus framework is proposed for a class of linear multiagent systems subject to matched and unmatched uncertainties in an undirected topology. A linear coordinate transformation is derived so that the consensus protocol design can be conveniently performed. The distributed consensus protocol is developed by using an integral sliding mode strategy. Consensus is achieved asymptotically and all subsystem states are bounded. By using an integral sliding mode control, the subsystems lie on the sliding surface from the initial time, which avoids any sensitivity to uncertainties during the reaching phase. By use of an appropriate projection matrix, the size of the equivalent control required to maintain sliding is reduced which reduces the conservatism of the design. MATLAB simulations validate the effectiveness and superiority of the proposed method

Inbuilt Tendency of the eIF2 Regulatory System to Counteract Uncertainties

Eukaryotic initiation factor 2 (eIF2) plays a fundamental role in the regulation of protein synthesis. Investigations have revealed that the regulation of eIF2 is robust against intrinsic uncertainties and is able to efficiently counteract them. The robustness properties of the eIF2 pathway against intrinsic disturbances is also well known. However the reasons for this ability to counteract stresses is less well understood. In this article, the robustness conferring properties of the eIF2 dependent regulatory system is explored with the help of a mathematical model. The novelty of the work presented in this article lies in articulating the possible reason behind the inbuilt robustness of the highly engineered eIF2 system against intrinsic perturbations. Our investigations reveal that the robust nature of the eIF2 pathway may originate from the existence of an attractive natural sliding surface within the system satisfying reaching and sliding conditions that are well established in the domain of control engineering

Real-time counting of single electron tunneling through a T-shaped double quantum dot system

Real-time detection of single electron tunneling through a T-shaped double quantum dot is simulated, based on a Monte Carlo scheme. The double dot is embedded in a dissipative environment and the presence of electrons on the double dot is detected with a nearby quantum point contact. We demonstrate directly the bunching behavior in electron transport, which leads eventually to a super-Poissonian noise. Particularly, in the context of full counting statistics, we investigate the essential difference between the dephasing mechanisms induced by the quantum point contact detection and the coupling to the external phonon bath. A number of intriguing noise features associated with various transport mechanisms are revealed.Comment: 8 pages, 5 figure

Rough paths in idealized financial markets

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.Comment: 21 pages, this version adds (in Appendix C) a reference to new results in the foundations of game-theoretic probability based on Hardin and Taylor's work on hat puzzle