Stability orthogonal regression for system identification

Tang, Xiaoquan; Zhang, Long

doi:10.1016/j.sysconle.2018.05.002

Cited by 5 publications

(4 citation statements)

References 11 publications

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“…As mentioned above, the optimal solution of the regression problem (5) satisfies all these three conditions in Lemma 2 and Lemma 1 is a special case of Lemma 2 with G = I. Therefore, similar with the problem (14), the solution of the problem (5) is unique.…”

Section: Proof Of Lemmamentioning

confidence: 80%

“…Lemma 1: The solution uniqueness of Lasso problem [11] 1. Vector Θ ∈ R M is an optimal solution of the problem (14) if and only if there exists a subgradient vector z which satisfies P T P( Θ − Θ * ) − P T ξ + λz = 0.…”

Section: The Uniqueness Of Solutionmentioning

confidence: 99%

“…where ρ is predetermined. ρ should be carefully tuned since it is related to noise and has a critical effect on selecting terms [14]. The second method is Lasso which is an effective method to obtain a sparse solution.…”

Section: Simulationmentioning

confidence: 99%

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Bayesian augmented Lagrangian algorithm for system identification

Tang

Zhang

2018

Systems & Control Letters

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Nonlinear Auto-Regressive model with eXogenous input (NARX) is one of the most popular black-box model classes that can describe many nonlinear systems. The structure determination is the most challenging and important part during the system identification. NARX can be formulated as a linear-in-the-parameters model, then the identification problem can be solved to obtain a sparse solution from the viewpoint of the weighted l 1 minimization problem. Such an optimization problem not only minimizes the sum squares of model errors but also the sum of reweighted model parameters. In this paper, a novel algorithm named Bayesian Augmented Lagrangian Algorithm (BAL) is proposed to solve the weighted l 1 minimization problem, which is able to obtain a sparse solution and enjoys fast computation. This is achieved by converting the original optimization problem into distributed suboptimization problems solved separately and penalising the overall complex model to avoid overfitting under the Bayesian framework. The regularization parameter is also iteratively updated to obtain a satisfied solution. In particular, a solver with guaranteed convergence is constructed and the corresponding theoretical proof is given. Two numerical examples have been used to demonstrate the effectiveness of the proposed method in comparison to several popular methods.

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Section: Proof Of Lemmamentioning

confidence: 80%

Section: The Uniqueness Of Solutionmentioning

confidence: 99%

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Bayesian augmented Lagrangian algorithm for system identification

Tang

Zhang

2018

Systems & Control Letters

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“…Over the years, this notion of the original OFR approach has been refined to further improve the search performance. These include OFR approaches with either new term evaluation criteria [17][18][19][20] or improved search strategies [21][22][23][24][25]. A detailed treatment on this subject can be found in the recent investigation by the authors [25].…”

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confidence: 99%

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

2020

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The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which include preference handling, Multi-Objective Evolutionary Algorithms (MOEAs) and a posteriori selection. To this end, three well-known MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to determine if there exists any significant difference in their search performance. The sensitivity of all these MOEAs to various qualitative and quantitative parameters, such as the choice of recombination mechanism, crossover and mutation probabilities, is also studied. These issues are critically analyzed considering seven discretetime and a continuous-time benchmark nonlinear system as well as a practical case study of non-linear wave-force modeling. The results of this investigation demonstrate that MOEAs can be tailored to determine the correct structure of nonlinear systems. Further, it has been established through frequency domain analysis that it is possible to identify multiple valid discrete-time models for continuous-time systems. A rigorous statistical analysis of MOEAs via performance sweet spots in the parameter space convincingly demonstrates that these algorithms are robust over a wide range of control parameters.of correct terms which captures the system dynamics is one of the major challenges of the system identification [6,7], and, therefore, is the main focus of this investigation.The exhaustive search to solve the structure selection problem is intractable even for moderate number of terms 'n', as this would require an evaluation of 2 n term subsets/structures. The structure selection problem is often 'NP-Hard' [13] and therefore requires an efficient search strategy. Since the search for system structure is primarily dependent on the limited number of observed data, it involves bias-variance trade-off [2, 3, 7], i.e., too sparse a structure may yield a high bias error (under-fitting) whereas a very complex structure may yield a high variance error (over-fitting). Further, earlier investigations [14,15] show that the over-fitted structures tend to induce 'ghost' dynamics which are not present in the actual system. Pursuing these arguments, it is clear that determination of the size of the identified structure (i.e., number of terms or 'cardinality') is a critical aspect of the structure selection process. However, this issue has received relatively less attention in the existing investigations.Among the existing structure selection approaches, the Orthogonal Forward Regression (OFR) proposed by Billings and Korenberg [16] has extensively been studied. It is a sequential model building approach in which the most significant term is added in each step, which is determined on the basis of a statistical criterion. Over the years, this notion of the original OFR approach has been refined to further improve the search performance. These include OFR approaches...

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Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems

2019

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The present study proposes a new structure selection approach for non-linear system identification based on Two-Dimensional particle swarms (2D-UPSO). The 2D learning framework essentially extends the learning dimension of the conventional particle swarms and explicitly incorporates the information about the cardinality, i.e., number of terms, into the search process. This property of the 2D-UPSO has been exploited to determine the correct structure of the non-linear systems. The efficacy of the proposed approach is demonstrated by considering several simulated benchmark nonlinear systems in discrete and in continuous domain. In addition, the proposed approach is applied to identify a parsimonious structure from practical non-linear wave-force data. The results of the comparative investigation with Genetic Algorithm (GA), Binary Particle Swarm Optimization (BPSO) and the classical Orthogonal Forward Regression (OFR) methods illustrate that the proposed 2D-UPSO could successfully detect the correct structure of the non-linear systems.

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Stability orthogonal regression for system identification

Cited by 5 publications

References 11 publications

Bayesian augmented Lagrangian algorithm for system identification

Bayesian augmented Lagrangian algorithm for system identification

Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation

Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems

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