Controller Design for Symbolic Input-Output Systems Using Feedforward Neural Networks

This was presented at 23rd IFAC World Congress (https://www.ifac2026.org/fairDash.do). Movies are not included due to the specifications of speakerdeck.

Transcript

1. Controller Design for Symbolic Input-Output Systems Using Feedforward Neural Networks Kohtaroh HIBINO∗, Eiji KONAKA (Meijo University, Japan)
2. Background Model-based Data-driven • Based on a mathematical model • Difficult to obtain for complex systems • Based on input-output data Hou, Wang (2013), From model-based control to data-driven control: Survey, classification and perspective. Information Sciences, 235, 3–35
3. Background: Related Work on DataDriven Control Design • Applicable in various settings depending on the input-output data type • Discrete inputs, continuous outputs → power converters, chemical plants • Konaka (2011) Design of discrete predictive controller using approximate nearest neighbor method. In Proc. of the 18th IFAC World Congress, 10213–10218. 𝑢(𝑘) 𝑦(𝑘) Plant 𝑢 ∈ 𝑈 = {−3, 0, 3}
4. Background: Symbolization • This study assumes a more restrictive setting • Relative magnitude and adjacency among values are unknown • The data are treated as symbols 𝑢(𝑘) 𝑦(𝑘) Plant 𝒖 ∈ 𝑈 = 1,0,0 , 0,1,0 , 0,0,1 𝒚 = 𝑌 ∈ { 1,0,0,0 , 0,1,0,0 , 0,0,1,0 , [0,0,0,1]}
5. Background: Objective • Objective: • Design a controller for symbolic input-output systems using a feedforward neural network 𝑢 𝑘 ∈𝑈 Plant Neural Controller 𝑦 𝑘 ∈𝑌
6. Problem Formulation: System Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Plant • Control system: Plant, Memory, Controller
7. Problem Formulation: Plant Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Plant • Input and output are symbolized 𝒖 ∈ 𝑈 = {𝒖 , 𝒖 , ⋯ 𝒖 } 𝒚 ∈ 𝑌 = {𝒚 , 𝒚 , ⋯ 𝒚 } • Order, magnitude, adjacency among symbols: Completely unknown
8. Plant Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Problem Formulation: Memories • Memories 𝑀 and 𝑀 stores past outputs and inputs 𝑴 (𝑛 = 3) 𝒚(𝑘) Outputs 𝑴 (𝑛 = 2) 𝒖(𝑘) Inputs 𝑘
9. Plant Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Problem Formulation: Controller • Input to controller: past I/O, reference output • Objective: choose 𝒖(𝑘) so that the output approaches the reference • Realized by a neural network
10. Training procedure • Data collection (1/2) Collect output sequence excited by random inputs 𝒖(𝑘) 𝑘 Input 𝒚(𝑘) Plant 𝑘 output
11. Training procedure • Data collection (2/2) Training data 𝒀 𝑘 = [𝒚 𝑘 , 𝒚 𝑘 − 1 , ⋯ 𝒚 (𝑘 − 𝑛 )] 𝑼 𝑘 = [𝒖 𝑘 − 1 , ⋯ 𝒖 (𝑘 − 𝑛 )] 𝒚 𝑘 = 𝒚 (𝑘) 𝒚 𝑘 = 𝒚 (𝑘 + 𝑛 ) Teaching data 𝒗 𝑘 = 𝒖 (𝑘) 𝑘 prediction horizon
12. Training procedure Controller • Training of neural controller • Collect a sufficiently long inputoutput symbol sequence • Check the frequency of output symbols; adjust the input pattern if needed • Train the neural network on the resulting sequence 𝒀 𝑘 𝑼 𝑘 𝒚 𝑘 𝒚 𝑘 ・ ・ ・ 𝒗 𝑘
13. Plant Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Numerical Experiments • Settings: Plant, Memory, Training procedure
14. Plant Memory 𝑴𝒚 Memory 𝑴𝒖 Controller Numerical Experiments: Plant (1/2) • Plant: nonlinear system 𝑥 𝑘+1 = +𝑢 𝑘 • 𝑢 𝑘 ∈ −0.7,0,0.7 𝑥 𝑘+1 =𝑥 𝑘 𝒚 𝑘 = 𝒉 𝑥 𝑘 ,𝑥 𝑘 • Two-dimensional extension of a discrete-time benchmark nonlinear model [Narendra & Parthasarathy, 1990]
15. Numerical Experiments: Plant (2/2) Definition of output symbol • Plant: nonlinear system 𝑥 𝑘+1 = • +𝑢 𝑘 𝑢 𝑘 ∈ −0.7,0,0.7 𝑥 𝑘+1 =𝑥 𝑘 𝒚 𝑘 = 𝒉 𝑥 𝑘 ,𝑥 𝑘 • Symbolization (left figure) • State vector to output symbol • The information of the plant is not used in training and control
16. Numerical Experiments: Data collection and Training Memory and Data Collection • Memory: 𝑛 = 1、𝑛 = 1 • 𝒀 (𝑘): 2 symbols, • 𝑼 𝑘 : 1 symbol • Selected by preliminary experiments (next slide) • 20000 samples of I/O sequence Collected Data (1000 samples)
17. 小中 英嗣4 k1 Numerical Experiments: Effect of Controller Order • Accuracy: (steps where 𝑦(𝑘) = 𝑦 (𝑘)) / total steps • 𝑛 = 𝑛 = 1, ⋯ , 10. 𝑛 = 2 • 50 random independent trials for each setting
18. スライド 17 小中 英嗣4 予稿Fig.6の図を右に配置して下さい． 小中 英嗣, k1 文字が小さいです． konaka, 2026/07/22
19. Numerical Experiments: Effect of Controller Order
20. Numerical Result: Trajectory • The output (red) can follow the reference (green) • Suitable input symbol is selected to achieve control objective • Accuracy: 92.25 % (369/400 samples)
21. Numerical Result: Transition and Convergence • Reference No.3 • Remain No.3 by switching input symbols
22. Numerical Result: Transition and Convergence • Reference No.3 • Remain No.3 by switching input symbols Controller design: Successful
23. Numerical Experiments: Structural Reconstruction Definition of output symbol • Extract symbol transitions from the trajectory → build an undirected graph • Reconstructed edges: {1,2}, {2,3}, {2,4}, {3,4} • Matches the adjacency of the original Voronoi partition
24. k2 Numerical Experiments: Structural Reconstruction Definition of output symbol • Extract symbol transitions from the trajectory → build an undirected graph • Reconstructed edges: {1,2}, {2,3}, {2,4}, {3,4} • Matches the adjacency of the original Voronoi partition Reconstructed graph
25. スライド 23 k2 右図の出力定義の点同士を青ではないわかりやすい色で結んだグラフを作る． konaka, 2026/07/22
26. Discussion and Conclusion Discussion Conclusion • Output successfully tracked the given reference • Trained neural controller reconstructed the implicit magnitude/adjacency relationships among symbols • Designed a controller for symbolic I/O systems using a neural network • Future work: real-world applications, automating design parameters