In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems...
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ISBN:
(纸本)9781612848006
In this paper nonlinear time-varying and bilinear discrete-time systems with additive bounded disturbances are considered. First, conditions guaranteeing uniform ultimate boundedness for time-varying nonlinear systems are established. Then, algebraic conditions ensuring the existence of polyhedral Lyapunov functions, uniform boundedness and positive invariance for closed-loop bilinear systems are obtained. Finally, these results are applied to various robust stabilization problems for bilinear systems subject to persistent additive disturbances. It is shown that these problems can be reduced to a single or a series of linear programming problems.
The Discrete Cosine Transform (DCT) is one of the most widely used techniques for image compression. Several algorithms are proposed to implement the DCT-2D. The scaled SDCT algorithm is an optimization of the DCT-1D,...
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Experiment design for quantum channel parameter estimation includes the design of the quantum input to the channel and the observables to be applied on the resulting quantum output system, called the experiment config...
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We propose a general methodology for performing statistical inference within a 'rare-events regime' that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish co...
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ISBN:
(纸本)9781457718175
We propose a general methodology for performing statistical inference within a 'rare-events regime' that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish consistent estimators for a very large class of canonical estimation problems, in a large alphabet setting. These include the problems studied in the original paper, such as entropy and probability estimation, in addition to many other interesting ones. We particularly illustrate this approach by consistently estimating the size of the alphabet and the range of the probabilities. We start by proposing an abstract methodology based on constructing a probability measure with the desired asymptotic properties. We then demonstrate two concrete constructions by casting the Good-Turing estimator as a pseudo-empirical measure, and by using the theory of mixture model estimation.
This paper is concerned with optimal utilization of storage, characterization of the economic value of storage in the presence of ramp-rate constraints and stochastically-varying electricity prices, and characterizati...
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ISBN:
(纸本)9781612848006
This paper is concerned with optimal utilization of storage, characterization of the economic value of storage in the presence of ramp-rate constraints and stochastically-varying electricity prices, and characterization of the price elasticity of demand induced by optimal utilization of storage. The ramp constraints limit the charging and discharging rate of storage, and can be due to the physical limitations of the storage device or the power lines. Such constraints make analytical characterization of optimal policies particularly difficult. In this paper, the optimal utilization problem is addressed in a finite-horizon stochastic dynamic programming framework, and an analytical characterization of the value function along with recursive formulas for computation of the associated optimal policy are derived. It is shown that the value function associated with the dynamic programming problem is a piecewise linear convex function of the storage state, i.e., the amount of stored energy. Furthermore, while the economic value of storage capacity is a non-decreasing function of price volatility, it is shown that due to finite ramping rates, the value of storage saturates quickly as the capacity increases, regardless of price volatility. Finally, it is shown that optimal utilization of storage by consumers could induce a considerable amount of price elasticity, particularly near the average price.
Abstract In this paper the concept of set invariance for time-delay systems is introduced with a specific attention to the linear discrete-time case. We are interested in the definition of a D(elay) -invariant set wit...
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Abstract In this paper the concept of set invariance for time-delay systems is introduced with a specific attention to the linear discrete-time case. We are interested in the definition of a D(elay) -invariant set with respect to a bounded polyhedral subset of the state-space. D -invariance conditions are derived based on the Minkowski addition in a first stage, and subsequently translated in feasibility-based tests in order to obtain an efficient computation time
In this paper, a low power and fast DCT (Discrete Cosine Transform) using multiplier-less method is presented with a new modified FGA (Flow-Graph Algorithm), which is derived from our previously presented FGA of DCT b...
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This paper presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price elasticity of consumption induced by optimally shifting flexible ...
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ISBN:
(纸本)9781612848006
This paper presents a mathematical model of consumer behavior in response to stochastically-varying electricity prices, and a characterization of price elasticity of consumption induced by optimally shifting flexible demands within a fixed time window. The approach is based on deriving the optimal load-shifting policy through a finite horizon stochastic dynamic program, and the analysis is performed under both perfect and partial information about price distribution. An aggregate demand model is constructed from individual demands with random arrivals and random deadlines. Under this model, the aggregate demand becomes a function of price only, and thus allows for quantitative characterization of the utility of demand and price elasticity. While the demand for electricity is often deemed to be highly inelastic, it is shown in this paper that optimal load-shifting can create a considerable amount of price elasticity, even when the aggregate consumption over a long period remains constant.
A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and pr...
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A dynamical system can exhibit structure on multiple levels. Different system representations can capture different elements of a dynamical system's structure. We consider LTI input-output dynamical systems and present four representations of structure: complete computational structure, subsystem structure, signal structure, and input output sparsity structure. We then explore some of the mathematical relationships that relate these different representations of structure. In particular, we show that signal and subsystem structure are fundamentally different ways of representing system structure. A signal structure does not always specify a unique subsystem structure nor does subsystem structure always specify a unique signal structure. We illustrate these concepts with a numerical example.
In this paper, a quadruped robot is studied in bounding motion. A new simplified model of quadruped robot in bounding motion with four actuated and two unactuated joints is developed. The kinetic and potential energie...
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In this paper, a quadruped robot is studied in bounding motion. A new simplified model of quadruped robot in bounding motion with four actuated and two unactuated joints is developed. The kinetic and potential energies of the under-actuated mechanical model of the quadruped robot are obtained and the dynamics of the robot model is derived using the Lagrangian method. It is shown that the dynamical equation of the proposed simplified model belongs to a class of second-order nonholonomic mechanical systems. The main motivation of this paper is to obtain quadruped model in bounding motion such that one can apply different control methods directly or after transformation in the obtained dynamic equations. Utilizing MATLAB, dynamics of the planar model has been simulated in backward and forward states. Physical parameters of the Little-Dog robot as an instance of the quadruped robot are considered in simulation The simulation is without control and therefore is unstable but it illustrates robot's manner in bounding motion before instability.
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