Mauricio G. Cea

Sampling and sampled-data models

Physical systems typically evolve continuously whereas modern controllers and signal processing devices invariably operate in discrete time. Hence sampling arises as a cornerstone problem in essentially all aspects of modern systems science. This paper reviews various aspects of sampling of signals and systems. We argue that careful consideration must be given to sampling to obtain meaningful results when interconnecting a physical system to a computer for the purpose of data storage, signal processing, or control. We also take the opportunity to dispel several common misconceptions about sampling and sampled-data systems.

Stabilization of Systems Over Bit-Rate-Constrained Networked Control Architectures

We consider the problem of control of open-loop unstable systems over a networked control architecture. We focus on the case where the system state is measured and where control commands are transmitted over a fixed bit-rate channel. We describe a novel nonlinear decoder model predictive controller which utilizes 1 bit per sample. The required bit rate can then be adjusted by varying the number of samples per unit time. We establish practical stability for the algorithm. We also compare the minimum fixed bit rate required by our algorithm with known results on the minimum bit rate necessary to achieve stability.

An MPC-based nonlinear quantizer for bit rate constrained networked control problems with application to inner loop power control in WCDMA

Bit rate constraints are a major stumbling block in Networked Control. Despite several techniques to improve performance, such as encoder-decoder design, the achieved performance is typically poor when only a few bits are available. This problem appears explicitly in Universal Mobile Telecommunications Systems (UMTS) where the control channel in WCDMA is implemented with a 1-bit constraint. In this paper we propose a new approach to this problem. Instead of focusing on the design of an encoder-decoder system for inner loop power control, we change the paradigm and, instead, focus on the design of an MPC-based controller for a fixed nonlinear decoder. We present simulations showing that the new scheme offer s significant performance advantages relative to existing algorithms.

Opportunities and Challenges in the Application of Nonlinear MPC to Industrial Problems

Linear MPC has been a major success story in industry. Arguably this is due to its capacity to deal with constraints and its seamless treatment of multivariable problems. Nonlinear MPC has also been extensively studied and advocated as a practical control strategy for processes whose dynamics are inherently nonlinear. In this paper we examine two industrial case studies to illustrate the power of nonlinear MPC in practice. We also use these case studies to point to future research challenges and opportunities.

Linear and nonlinear decoupling for inner loop power control in 3G mobile communications

Abstract Inner loop power control is a crucial part of the operation of 3G mobile communication systems. This is necessary to deal with the, so called, ‘near-far’ problem and to combat the effects of time variations in the channel gain. In practice, power control is dealt with in a decentralized fashion, i.e., using one SISO control loop for each user. However, significant multivariable coupling occurs due to the fact that each user is a source of interference to every other user. This means that the actual performance is significantly degraded relative to the idealized SISO case. In this paper, we describe a novel nonlinear decoupling algorithm for the uplink of the WCDMA 3G cellular system which effectively compensates for the MIMO interactions. We also develop a simplified linearized form of the algorithm. We explore the relative merits of the scheme for typical mobile communication scenarios incorporating grant changes, fading and quantization. Our simulations show that, in all cases, the decoupling strategies lead to significant performance gains relative to the use of decentralized strategies in common use.

Model Predictive Zooming Power Control in Future Cellular Systems under Coarse Quantization

Control signal encoding results in coarse quantization impairments in todays cellular power control loops. The paper proposes a new approach for future cellular systems that enhances performance whilest retaining coarse quantization of the power control signal. The design applies novel optimal model predictive control (MPC) techniques in the base station, based on a model of an adaptive quantization zooming controller in the UE. This allows a high bandwidth with respect to set point changes and disturbances, at the same time as the quantization noise in stationary situations is minimized.

A Novel Technique based on up-sampling for addressing Modeling Issues in Sampled Data Nonlinear Filtering

Abstract We address sampled data non-linear filtering problems where there is an underlying continuous-time system. In the case of linear systems, it is well known that there is an exact discrete model that describes the second order properties at the sampling instants. However, in the nonlinear case, one must use an approximate model. In practice, simple Euler expansions are typically used. However, an Euler model is known to give a poor approximation especially with moderate sample period. Here we propose a resolution of this difficulty via the use of an up-sampling strategy. We show that, as the up-sampling rate increases, then in the linear case the up-sampled filter converges to the true filter. We illustrate by an example.

Control with communication constraints

An emerging area of importance in control science is that of networked control. Within this framework one considers the impact of communication constraints on the performance of feedback control systems. The topic bridges the traditional areas of control, communications and information theory. In this paper we will focus on the practical application of these ideas. Perhaps unsurprisingly, a major area of application arises in the control of communication systems themselves since, here, the control commands and measurements are invariably sent over the same communication channels as are used for data. These channels are subject to imperfections including quantization, lost packets, random delays and decentralized architectures. Hence the associated control problems are quintessential examples of control subject to communication constraints. The paper will review several of these problems and point to future research challenges.

Design of scenarios for constrained stochastic optimization via vector quantization

Probabilistic methods have recently emerged as an exciting new approach for dealing with uncertainty in stochastic optimization problems. These methods depend upon the selection of a set of scenarios to represent the uncertain variables. Typically these scenarios are obtained by making random drawings from the underlying probability distribution. Here we examine alternative approaches in which the scenarios are targeted at the underlying problem. In particular, we explore the use of vector quantization methods for scenario generation. Vector quantization based scenarios are more computationally intensive to generate but offer advantages for certain classes of optimization problems. Several examples are presented to illustrate the ideas.

Application of Minimum Distortion Filtering to Identification of Linear Systems Having Non-uniform Sampling Period

We consider the problem of identification of continuous time systems when the data is collected using non-uniform sampling periods. We formulate this problem in the context of Nonlinear Filtering. We show how a new class of nonlinear filtering algorithm (Minimum Distortion Filtering) can be applied to this problem. A simple example is used to illustrate the performance of the algorithm. We also compare the results with those obtained from (a particular realization) of Particle Filtering.