Tinbergen and Theil Meet Nash: Controllability in Policy Games

This paper generalizes the classical theory of economic policy to a static LQ-strategic context between n players. We show how this generalized version of controllability can profitably be used to deal with policy ineffectiveness issues and Nash equilibrium existence.Policy games, policy ineffectiveness, static controllability, Nash equilibrium existence

Stochastic and Optimal Distributed Control for Energy Optimization and Spatially Invariant Systems

Improving energy efficiency and grid responsiveness of buildings requires sensing, computing and communication to enable stochastic decision-making and distributed operations. Optimal control synthesis plays a significant role in dealing with the complexity and uncertainty associated with the energy systems. The dissertation studies general area of complex networked systems that consist of interconnected components and usually operate in uncertain environments. Specifically, the contents of this dissertation include tools using stochastic and optimal distributed control to overcome these challenges and improve the sustainability of electric energy systems. The first tool is developed as a unifying stochastic control approach for improving energy efficiency while meeting probabilistic constraints. This algorithm is applied to demonstrate energy efficiency improvement in buildings and improving operational efficiency of virtualized web servers, respectively. Although all the optimization in this technique is in the form of convex optimization, it heavily relies on semidefinite programming (SP). A generic SP solver can handle only up to hundreds of variables. This being said, for a large scale system, the existing off-the-shelf algorithms may not be an appropriate tool for optimal control. Therefore, in the sequel I will exploit optimization in a distributed way. The second tool is itself a concrete study which is optimal distributed control for spatially invariant systems. Spatially invariance means the dynamics of the system do not vary as we translate along some spatial axis. The optimal H2 [H-2] decentralized control problem is solved by computing an orthogonal projection on a class of Youla parameters with a decentralized structure. Optimal H∞ [H-infinity] performance is posed as a distance minimization in a general L∞ [L-infinity] space from a vector function to a subspace with a mixed L∞ and H∞ space structure. In this framework, the dual and pre-dual formulations lead to finite dimensional convex optimizations which approximate the optimal solution within desired accuracy. Furthermore, a mixed L2 [L-2] /H∞ synthesis problem for spatially invariant systems as trade-offs between transient performance and robustness. Finally, we pursue to deal with a more general networked system, i.e. the Non-Markovian decentralized stochastic control problem, using stochastic maximum principle via Malliavin Calculus

Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Scalable hardware memory disambiguation

This dissertation deals with one of the long-standing problems in Computer Architecture – the problem of memory disambiguation. Microprocessors typically reorder memory instructions during execution to improve concurrency. Such microprocessors use hardware memory structures for memory disambiguation, known as LoadStore Queues (LSQs), to ensure that memory instruction dependences are satisfied even when the memory instructions execute out-of-order. A typical LSQ implementation (circa 2006) holds all in-flight memory instructions in a physically centralized LSQ and performs a fully associative search on all buffered instructions to ensure that memory dependences are satisfied. These LSQ implementations do not scale because they use large, fully associative structures, which are known to be slow and power hungry. The increasing trend towards distributed microarchitectures further exacerbates these problems. As on-chip wire delays increase and high-performance processors become necessarily distributed, centralized structures such as the LSQ can limit scalability. This dissertation describes techniques to create scalable LSQs in both centralized and distributed microarchitectures. The problems and solutions described in this thesis are motivated and validated by real system designs. The dissertation starts with a description of the partitioned primary memory system of the TRIPS processor, of which the LSQ is an important component, and then through a series of optimizations describes how the power, area, and centralization problems of the LSQ can be solved with minor performance losses (if at all) even for large number of in flight memory instructions. The four solutions described in this dissertation — partitioning, filtering, late binding and efficient overflow management — enable power-, area-efficient, distributed and scalable LSQs, which in turn enable aggressive large-window processors capable of simultaneously executing thousands of instructions. To mitigate the power problem, we replaced the power-hungry, fully associative search with a power-efficient hash table lookup using a simple address-based Bloom filter. Bloom filters are probabilistic data structures used for testing set membership and can be used to quickly check if an instruction with the same data address is likely to be found in the LSQ without performing the associative search. Bloom filters typically eliminate more than 80% of the associative searches and they are highly effective because in most programs, it is uncommon for loads and stores to have the same data address and be in execution simultaneously. To rectify the area problem, we observe the fact that only a small fraction of all memory instructions are dependent, that only such dependent instructions need to be buffered in the LSQ, and that these instructions need to be in the LSQ only for certain parts of the pipelined execution. We propose two mechanisms to exploit these observations. The first mechanism, area filtering, is a hardware mechanism that couples Bloom filters and dependence predictors to dynamically identify and buffer only those instructions which are likely to be dependent. The second mechanism, late binding, reduces the occupancy and hence size of the LSQ. Both of these optimizations allows the number of LSQ slots to be reduced by up to one-half compared to a traditional organization without any performance degradation. Finally, we describe a new decentralized LSQ design for handling LSQ structural hazards in distributed microarchitectures. Decentralization of LSQs, and to a large extent distributed microarchitectures with memory speculation, has proved to be impractical because of the high performance penalties associated with the mechanisms for dealing with hazards. To solve this problem, we applied classic flow-control techniques from interconnection networks for handling resource con- flicts. The first method, memory-side buffering, buffers the overflowing instructions in a separate buffer near the LSQs. The second scheme, execution-side NACKing, sends the overflowing instruction back to the issue window from which it is later re-issued. The third scheme, network buffering, uses the buffers in the interconnection network between the execution units and memory to hold instructions when the LSQ is full, and uses virtual channel flow control to avoid deadlocks. The network buffering scheme is the most robust of all the overflow schemes and shows less than 1% performance degradation due to overflows for a subset of SPEC CPU 2000 and EEMBC benchmarks on a cycle-accurate simulator that closely models the TRIPS processor. The techniques proposed in this dissertation are independent, architectureneutral and their cumulative benefits result in LSQs that can be partitioned at a fine granularity and have low design complexity. Each of these partitions selectively buffers only memory instructions with true dependences and can be closely coupled with the execution units thus minimizing power, area, and latency. Such LSQ designs with near-ideal characteristics are well suited for microarchitectures with thousands of instructions in-flight and may enable even more aggressive microarchitectures in the future.Computer Science

Dynamic Controllability with Overlapping targets: A Generalization of the Tinbergen-Nash Theory of Economic Policy

We generalize some recent results developed in static policy games with multiple players, to a dynamic context. We find that the classical theory of economic policy can be usefully applied to a strategic context of difference games: if one player satisfies the Golden Rule, then either all other players’ policies are ineffective with respect to the dynamic target variables shared with that player; or no Nash Feedback Equilibrium can exist, unless they all share target values for those variables. We extend those results to the case where there are also non-dynamic targets, to show that policy effectiveness (a Nash equilibrium) can continue to exist if some players satisfy the Golden Rule but target values differ between players in the non-dynamic targets. We demonstrate the practical importance of these results by showing how policy effectiveness (a policy equilibrium) can appear or disappear with small variations in the expectations process or policy rule in a widely used model of monetary policy.Policy games, Policy ineffectiveness, Static controllability, Existence of equilibria, Nash feedback equilibrium

Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models

This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show how our approach reduces the analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We explicitly show the existence of a non-empty Turing space of diffusive instability by developing a linear-quadratic approximation of the original non-linear problem. We apply our method to a bioeconomic problem, but the method has more general economic applications where spatial considerations and pattern formation are important. We believe that the extension of Turing analysis and the theory associated with the dispersion relationship to recursive infinite horizon optimal control settings is new.Spatial analysis, Pattern formation, Turing mechanism, Turing space, Pontryagin’s principle, Bioeconomics