Swapping Design Research Articles

Composite Learning Based Adaptive Control of Linear 2×2 Hyperbolic PDE Systems.

This article considers the adaptive stability control of a class of 2×2 linear hyperbolic PDE systems. The PDE model is subject to constant but in-domain and boundary unknown parameters. A novel adaptive controller is developed by leveraging the swapping design technique and composite parameter learning law. With swapping design, several linear and static combinations, including carefully designed filters, unknown parameters, and error terms, are constructed to express the system states. From the static combinations, a composite learning based forgetting-factor least squares law is introduced to guarantee exponential parameter convergence without the persistent excitation (PE). Although inaccurate parameter estimation in the adaptive backstepping control results in asymptotic stability of the system, accurate parameter estimation ensures the exponential convergence of closed-loop system and concomitantly improves the transient performance. Finally, a comparative numerical simulation is performed to validate the effectiveness and advantage of the developed adaptive control scheme.

Adaptive control of linear[formula omitted] hyperbolic systems

We design two closely related state feedback adaptive control laws for stabilization of a class of2×2 linear hyperbolic system of partial differential equations (PDEs) with constant but uncertain in-domain and boundary parameters. One control law uses an identifier, while the other is based on swapping design. We establish boundedness of all signals in the closed loop system, pointwise in space and time, and convergence of the system states to zero pointwise in space. The theory is demonstrated in simulations.

Word- and Partition-Level Write Variation Reduction for Improving Non-Volatile Cache Lifetime

Non-volatile memory technologies are among the most promising technologies for implementing the main memories and caches in future microprocessors and replacing the traditional DRAM and SRAM technologies. However, one of the most challenging design issues of the non-volatile memory technologies is the limited write. In this article, we first propose to exploit the narrow-width values to improve the lifetime of non-volatile last-level caches with word-level write variation reduction. Leading zeros masking scheme is proposed to reduce the write stress to the upper half of the narrow-width data. To balance the write variations between the upper half and the lower half of the narrow-width data, two swapping schemes, the swap on write (SW) and swap on replacement (SRepl), are proposed. Two existing optimization schemes, the multiple dirty bit (MDB) and read before write (RBW), are adopted with our word-level swapping design. To further reduce the write variation on the partition level, we propose to exploit the cache partitioning design to improve the lifetime. Based on the observation that different applications demonstrate different cache access (write) behaviors, we propose to partition the last-level cache for different applications and balance the write variations by partition swapping. Both software-based and hardware-based partitioning and swapping schemes are proposed and evaluated for different situations. Our experimental results show that both our word- and partition-level designs can improve the lifetime of the non-volatile caches effectively with low performance and energy overheads.

Estimation of boundary parameters in general heterodirectional linear hyperbolic systems

In this paper, we extend recent results on state and boundary parameter estimation in coupled systems of linear partial differential equations (PDEs) of the hyperbolic type consisting of n rightward and one leftward convecting equations, to the general case which involves an arbitrary number of PDEs convecting in both directions. Two adaptive observers are derived based on swapping design, where one introduces a set of filters that can be used to express the system states as linear, static combinations of the filter states and the unknown parameters. Standard parameter identification laws can then be applied to estimate the unknown parameters. One observer which requires sensing at both boundaries, generates estimates of the boundary parameters and system states, while the second observer estimates the parameters from sensing limited to the boundary anti-collocated with the uncertain parameters. Proof of boundedness of the adaptive laws is offered, and sufficient conditions ensuring exponential convergence are derived. The theory is verified in simulations.

Adaptive stabilization of [formula omitted] coupled linear hyperbolic systems with uncertain boundary parameters using boundary sensing

We design an adaptive control law stabilizing a class of systems of the form of n+1 linear partial differential equations (PDEs) of the hyperbolic type from boundary sensing only. We do this by combining a recently derived observer based on swapping design, with a backstepping-based adaptive control law with time-varying gains. Boundedness of all signals in the closed loop system and asymptotic convergence to zero pointwise in space for the system states are proved. The theory is demonstrated in a simulation.

An Adaptive Observer Design for $n+1$ Coupled Linear Hyperbolic PDEs Based on Swapping

In this paper, we use swapping design filters to bring systems of $n+1$ partial differential equations of the hyperbolic type to static form. Standard parameter identification laws can then be applied to estimate unknown parameters in the boundary conditions. Proof of boundedness of the adaptive laws are offered, and the results are demonstrated in simulations.

Boundary Parameter and State Estimation in General Linear Hyperbolic PDEs

We develop an adaptive observer that estimates boundary parameters and the system states in general heterodirectional linear systems of m+n coupled hyperbolic partial differential equations. The observer uses boundary sensing only, and is based on the swapping design, where filters are constructed that can be used to express the system states as linear static combinations of the unknown parameters and the filters states. Standard parameter identification laws can then be applied. Proof of boundedness of the estimates is offered, and sufficient conditions ensuring exponential convergence to their true values is derived. The theory is verified in a simulation.

Adaptive control of PDEs

This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed—the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reaction–advection–diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.

ADAPTIVE CONTROL OF PDES

This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed—the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reaction-advection-diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.

ADAPTIVE CONTROL OF PDES

This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed—the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reaction-advection-diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.