Closed-form expressions of convex combinations

The control of linear parameter-varying (LPV) systems with time-varying real uncertain parameters, where only some of the parameters are measured and available for feedback, is considered. The control objectives are internal stability and disturbance attenuation in the sense of a bounded induced L/sub 2/-norm from the disturbance to the controlled output. Using parametric Lyapunov functions, the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities (LMIs) and an additional coupling constraint which destroys the convexity of the overall problem. By transforming the coupling constraint into a rank condition, the problem is recast into a rank-minimization problem with LMI constraints. An example is included that demonstrates the application of the results.

In this paper, the control of linear parameter-varying (LPV) systems with time-varying real uncertain parameters, where only some of the parameters are measured and available for feedback is considered. The control objectives are internal stability and disturbance attenuation in the sense of a bounded induced L/sub 2/-norm from the external disturbance to the controlled output of the system. Using parametric Lyapunov functions, the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities (LMI) and an additional coupling constraint which destroys the convexity of the overall problem. Hence, by transforming the coupling constraint into a rank condition, the problem is recast into a rank-minimization problem with LMI constraints. An algorithm based on the alternating projections method is proposed. Although the convergence of the algorithm is not guaranteed, an example is included that demonstrates the application of the results.

On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems

The state consensus problem among groups of linear parameter-varying (LPV) systems is addressed. The systems are assumed to have an identical LPV structure. We consider both homogeneous groups, where the time-varying parameters are identical, and heterogeneous groups, where the parameters can be different for all agents. Motivated by relative sensing we assume static, possibly parameter-varying, diffusive couplings between neighboring agents. We provide necessary and sufficient conditions for state consensus and, in the homogeneous case, present design procedures for the coupling gains based on linear matrix inequalities.

In this paper, we address a synthesis problem of the parameter-dependent output feedback H∞ control for linear parameter-varying systems with time-delay. The scheme adopts the parameter-dependent past state information to construct the dynamic output feedback controller. In this case, on basis of the quadratic Lyapunov functional with parameter-dependence, we analyze the parameter-dependent H∞ stability conditions for the closed-loop time-delayed linear parameter-varying system in terms of linear matrix inequalities. However, this stability condition is of an infinite-dimension. To derive computationally tractable criteria for the dynamic output feedback controller, several slack variables and a convex relaxation technique are employed to have the infinite-dimensional condition of linear matrix inequalities cast into a finite dimensional convex optimization problem. By solving the convex optimization problem, we harvest the dynamic output feedback controller with memory for the time-delayed linear parameter-varying system. Finally, two examples are included to illustrate the effectiveness of the proposed approach.

A closed-form approach for the resonant frequency analysis of clamped rectangular microplates under distributed electrostatic force

Linear parameter-varying (LPV) modeling is a powerful framework for representing time-varying systems as well as nonlinear dynamics in terms of a linear structure dependent on a time-varying parameter known as the scheduling parameter. Combining model predictive control (MPC) with LPV predictors (LPVMPC) results in an efficient parameter-dependent MPC approach. However, the future trajectory of the scheduling parameter required for formulating the LPVMPC optimization problem is not known in advance. In this paper, a Bayesian nonparametric approach within Gaussian process (GP) regression framework is introduced to predict the future behavior of the scheduling parameter over the MPC prediction horizon, which can be exploited by the proposed LPVMPC approach. The performance of the presented approach, i.e., GP-LPVMPC, is tested on a simulation example, where it is demonstrated that it outperforms the LPVMPC when the scheduling variable is frozen over the MPC prediction horizon in terms of convergence and control performance.

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.

This paper develops the stability analysis and delay-dependent \(\mathcal {H}_{\infty }\) control synthesis for linear parameter-varying (LPV) systems with time-varying state delays. On the basis of the Finsler’s lemma, sufficient conditions on \(\mathcal {H}_{\infty }\) performance analysis are formulated in terms of parameterized linear matrix inequalities. The interesting annihilator matrix is constituted by time-varying parameters of LPV systems to reduce the conservatism. A numerical example is presented to confirm the efficiency of the proposed method.

This article presents the central finite-dimensional H ∞ controller for linear time-varying systems with unknown parameters, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding H 2 controller problem, using the technique proposed in Doyle et al. [Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H Infinity Control Problems’, IEEE Transactions Automatic Control, 34, 831–847]. This article yields the central suboptimal H ∞ controller for linear systems with unknown parameters in a closed finite-dimensional form, based on the corresponding H 2 controller obtained in Basin and Calderon-Alvarez [Basin, M.V., and Calderon-Alvarez, D. (2008), ‘Optimal LQG Controller for Linear Systems with Unknown Parameters’, Journal of The Franklin Institute, 345, 293–302]. Numerical simulations are conducted to verify performance of the designed central suboptimal controller for uncertain linear systems with unknown parameters against the conventional central suboptimal H ∞ controller for linear systems with exactly known parameter values.

Bandwidth efficient optimal superimposed pilot design for channel estimation in OSTBC based MIMO–OFDM systems

An analytical closed-form expression is derived for the shear correction factor of beams with annular cross sections. The beam theory is formulated using the variational asymptotic method, which uses inherently occurring small parameters to convert a variational statement from three-dimensional elasticity to an engineering beam theory without any ad hoc assumptions on the beam kinematics. Comparisons are made with existing solutions in the literature; then, the critical speeds of a rotor are shown to depend not only on the inclusion of transverse shear but also on the choice of the shear correction factor, establishing its importance. The motivation of this work is twofold: first, rotors that can be modeled as beams with annular cross sections are often encountered, and this expression for the shear correction factor can be readily incorporated into any rotor dynamics solver; and second, closed-form expressions, when available, always provide more insight into structural mechanics as opposed to numerical solutions.

A new optical method is presented for measurement of the bulk lifetime τ and surface recombination velocity S in semiconductors. The method is based on measurement of the photoluminescence decay as a function of the self-absorption under different excitation conditions. Closed-form analytical expressions, accounting for the self-absorption, are derived for the photoluminescence decay for a semi-infinite sample with an arbitrary value of S. A comprehensive method based on the analytical expressions is devised for the nondestructive extraction of the parameters in bulk wafers. The technique is particularly suitable for characterization of the surface passivation of compound semiconductors with a direct band gap, and is demonstrated on a GaAs sample. Application of the technique for characterization of indirect band gap semiconductors is also discussed.

The current-voltage characteristics of the photovoltaic module are highly non-linear and depend, among other factors, on solar insolation level and on the module surface temperature. At a fixed value of insolation level to which the module is subjected, the terminal voltage decreases non-linearly as the load current increases. Most previous research in this area depends on non-linear mathematical equations relating the module voltage with its current. Therefore, numerical methods of analysis are required to determine the performance of a system in which a photovoltaic module, or array, is an element. It is known that most operating points in such systems lie in the range between the no-load voltage and the maximum power point voltage of the photovoltaic module. In this article, an approach is presented to obtain approximate closed-form analytical expressions for the current-voltage characteristics of any photovoltaic array in the range from no-load condition up to the maximum power point condition. The technique presented allows the direct method to predict the operating conditions of photovoltaic arrays when feeding loads, such as DC motors, without using tedious and time-consuming iterative numerical techniques, and the approximated current-voltage characteristics obtained analytically are compared with corresponding exact characteristics, with very close agreement obtained. To validate the proposed closed-form analytical expressions of the current-voltage characteristics of the photovoltaic array when feeding DC motors, the torque speed characteristics of different types of DC motors are obtained analytically and compared with the corresponding exact characteristics. The difference between the approximate and exact characteristics is very small.

Presents an alternative approach to solve robust performance problems for linear parameter-varying (LPV) control systems. In contrast to previous methods, which are focused on deterministic algorithms, this paper is based on a probabilistic setting. The proposed randomized algorithm provides a sequence of candidate solutions converging with probability one to a feasible solution in a finite number of steps. The main advantages of this method over the previous literature are as follows: (i) the randomized algorithm gives a direct method for general LPV plants with state-space matrices depending on scheduling parameters in a nonlinear manner, i.e. the probabilistic setting does not require any approximation, such as a linear fractional transformation (LFT), of the state space matrices or a gridding on the set of scheduling parameters; (ii) the proposed algorithm is sequential and, at each iteration, it does not require heavy computational effort, such as simultaneously solving a large number of linear matrix inequalities.