_ + _ https://jp.mathworks.com/academia/courseware/mass-spring-damper-systems.html <latexit sha1_base64="fNVoAq7bnV7VURo3ZBbHY5ydDtM=">AAACGXicbZDLSgMxFIYzXmu9jboSN8EiCEKZEa1uhIIgLivYC7RDyWTSNjQzGZIz0jIUH8S1W30Gd+LWlY/gW5i2s9DWHwIf/zknyfn9WHANjvNlLSwuLa+s5tby6xubW9v2zm5Ny0RRVqVSSNXwiWaCR6wKHARrxIqR0Bes7vevx/X6A1Oay+gehjHzQtKNeIdTAsZq2/thKwgkpIPRCW1l0B/gK3zTtgtO0ZkIz4ObQQFlqrTtb3MBTUIWARVE66brxOClRAGngo3yrUSzmNA+6bKmwYiETHvpZIURPjJOgDtSmRMBnri/J1ISaj0MfdMZEujp2drY/Lc2dkBKoWc+AJ1LL+VRnACL6PT9TiIwSDyOCQdcMQpiaIBQxc0KmPaIIhRMmHmTjTubxDzUTotuqXh+d1Yol7KUcugAHaJj5KILVEa3qIKqiKJH9Ixe0Kv1ZL1Z79bHtHXBymb20B9Znz8R7aDV</latexit> m¨ x + c ˙ x + kx = F
Z T 0 kuk2dt, x(T) = xgoal <latexit sha1_base64="S4M4KDQK5QwGzIVe1MJc4O8DQQc=">AAACGHicbVDJSgNBEO1xjXGLehG8NAYhXsKMxOUY8OIxglkgE0JPpydp0tM9dtcIYRI/xLNX/QZv4tWbn+Bf2FkOmvig4PFeFVX1glhwA6775Swtr6yurWc2sptb2zu7ub39mlGJpqxKlVC6ERDDBJesChwEa8SakSgQrB70r8d+/YFpw5W8g0HMWhHpSh5ySsBK7dyhP0wKcOoP26nPZQiDEfYFu8deO5d3i+4EeJF4M5JHM1TauW+/o2gSMQlUEGOanhtDKyUaOBVslPUTw2JC+6TLmpZKEjHTSicfjPCJVTo4VNqWBDxRf0+kJDJmEAW2MyLQM/PeWPzXGyuglDBzB0B41Uq5jBNgkk73h4nAoPA4JdzhmlEQA0sI1dy+gGmPaELBZpm12XjzSSyS2lnRuyie35by5dIspQw6QseogDx0icroBlVQFVH0iJ7RC3p1npw35935mLYuObOZA/QHzucPDsGgSQ==</latexit> ku(t)k1 1 <latexit sha1_base64="1yVbZegkjjEuXl3/OOsvBmpWrOU=">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</latexit> J(x0) = Z T 0 dt, ku(t)k1 1 A B <latexit sha1_base64="xh4DQY8SILI18Bt6tNDzsjSfO9E=">AAACFXicbVDLSsNAFJ34rPUVFVduBotQNyWRUt0IBTcuK/QFbQiT6aQdOsmEmRtpCf0O1271G9yJW9d+gn/h9LHQ1gMXDufcy733BIngGhzny1pb39jc2s7t5Hf39g8O7aPjppapoqxBpZCqHRDNBI9ZAzgI1k4UI1EgWCsY3k391iNTmsu4DuOEeRHpxzzklICRfPt0VKxf3uKRn3WBjSDrSyImE98uOCVnBrxK3AUpoAVqvv3d7UmaRiwGKojWHddJwMuIAk4Fm+S7qWYJoUPSZx1DYxIx7WWz8yf4wig9HEplKgY8U39PZCTSehwFpjMiMNDL3lT815sqIKXQSwdAeONlPE5SYDGd7w9TgUHiaUS4xxWjIMaGEKq4eQHTAVGEggkyb7Jxl5NYJc2rklspVR7KhWp5kVIOnaFzVEQuukZVdI9qqIEoytAzekGv1pP1Zr1bH/PWNWsxc4L+wPr8AS4wn1s=</latexit> x(T) = xgoal
,up 1 p 1 X t=0 x> t Qxt + u> t Rut + x> p Qf xp <latexit sha1_base64="yiEw6RggZAsYi1UZg/GCYoCkC2I=">AAACKHicbZDLSgMxFIYz9VbrrerSTbAIhdYyI/WyEapuXFawF2jLkEnTNjQzGZIz0jL0FXwQ1271GdxJt+58C9PLQlt/CPx85xxOzu+Fgmuw7bGVWFldW99Ibqa2tnd299L7B1UtI0VZhUohVd0jmgkesApwEKweKkZ8T7Ca17+b1GtPTGkug0cYhqzlk27AO5wSMMhNZwduDDlnhK/xzcCF3G3kQh43MRhgG0PbEnQ+PHXcdMYu2FPhZePMTQbNVXbT3822pJHPAqCCaN1w7BBaMVHAqWCjVDPSLCS0T7qsYWxAfKZb8fSiET4xpI07UpkXAJ7S3xMx8bUe+p7p9An09GJtAv+tTQhIKfTCB6Bz1Yp5EEbAAjrb34kEBoknqeE2V4yCGBpDqOLmBEx7RBEKJtuUycZZTGLZVM8KzkXh/KGYKRXnKSXRETpGWeSgS1RC96iMKoiiZ/SK3tC79WJ9WJ/WeNaasOYzh+iPrK8fCfmkGA==</latexit> xt+1 = Axt + But, t = 0, · · · , p 1 <latexit sha1_base64="8Y8vH0VuwhjjI5U3nKgDqvwrUlw=">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</latexit> u = 2 6 4 u0 . . . up 1 3 7 5 x0 , Q, R, Qf <latexit sha1_base64="1irHdw9QUP/XzlFvEnHABXwSR0I=">AAACHnicbZDLSgMxFIYz9VbrbdSlIMEiCEKZkXpZFtx0WcFeoB1LJs20oZlkTM4IpXTng7h2q8/gTtzqI/gWppeFtv4Q+PjPOZycP0wEN+B5X05maXlldS27ntvY3NrecXf3akalmrIqVULpRkgME1yyKnAQrJFoRuJQsHrYvx7X6w9MG67kLQwSFsSkK3nEKQFrtd3DVsxlO8XpXQtUgsspPr2foiWs227eK3gT4UXwZ5BHM1Xa7nero2gaMwlUEGOavpdAMCQaOBVslGulhiWE9kmXNS1KEjMTDCd3jPCxdTo4Uto+CXji/p4YktiYQRzazphAz8zXxua/tbEDSgkz9wGIroIhl0kKTNLp/igVGBQeZ4U7XDMKYmCBUM3tCZj2iCYUbKI5m40/n8Qi1M4K/kXh/KaYLxVnKWXRATpCJ8hHl6iEyqiCqoiiR/SMXtCr8+S8Oe/Ox7Q148xm9tEfOZ8/StSh3Q==</latexit> min u u > Hu + q > u + r
dt), t = 0, · · · , p 1 <latexit sha1_base64="cSK7IBGNtFERol5QdtFCAX4YmyE=">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</latexit> for all dt 2 D, t = 0, · · · , p 1 xt 2 X, t = 1, · · · , p, ut 2 U, t = 0, · · · , p 1 <latexit sha1_base64="rMtRH3zW08HTFInouS4fD2pxhb4=">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</latexit> min u0,··· ,up 1 max dt,··· ,dp 1 p 1 X t=0 `t(xt, ut) + `p(xp)
t nu ny <latexit sha1_base64="udUyzllvGZeBO3hLkwUh8Qazu+E=">AAACIHicbVDLSsNAFJ34rPFVdelmsAguakmkVJcFN+Kqgn1AE8JkOm2HTmbCzI1QQrd+iGu3+g3uxKX+gX9h0nahrQcuHM65l3vvCWPBDTjOp7Wyura+sVnYsrd3dvf2iweHLaMSTVmTKqF0JySGCS5ZEzgI1ok1I1EoWDscXed++4Fpw5W8h3HM/IgMJO9zSiCTgiK2vYjLIE0Cp4w92lNgyjgJ0vjcnUzwrW0HxZJTcabAy8SdkxKaoxEUv72eoknEJFBBjOm6Tgx+SjRwKtjE9hLDYkJHZMC6GZUkYsZPp59M8Gmm9HBf6awk4Kn6eyIlkTHjKMw6IwJDs+jl4r9eroBSwiwcAP0rP+UyToBJOtvfTwQGhfO0cI9rRkGMM0Ko5tkLmA6JJhSyTPNs3MUklknrouLWKrW7aqlenadUQMfoBJ0hF12iOrpBDdREFD2iZ/SCXq0n6816tz5mrSvWfOYI/YH19QOgC6Hy</latexit> min u0,··· ,up 1 J f <latexit sha1_base64="dvn9iqzOCVqwOzeQq450TD6twDo=">AAACRHicbZDNSsNAFIUn/tb6V3XpZrAILdSSSFE3QkEXLitYFWwJk+mkHZzMhJkbMYS8kA/i2m19A8GduBWTtqC2Xhj4OOde7tzjhYIbsO2hNTe/sLi0XFgprq6tb2yWtravjYo0ZW2qhNK3HjFMcMnawEGw21AzEniC3Xj3Z7l/88C04UpeQRyybkD6kvucEsgkt3Qeu4BPsV+JXKjhDu0pMDUcuQkcSDdKazjO0Ul/vHjsxWn11K88ulAtFt1S2a7bo8Kz4EygjCbVcktvnZ6iUcAkUEGMuXPsELoJ0cCpYGmxExkWEnpP+uwuQ0kCZrrJ6NoU72dKD/tKZ08CHqm/JxISGBMHXtYZEBiYaS8X//VyBZQSZuoD4J90Ey7DCJik4/1+JDAonCeKe1wzCiLOgFDNsxMwHRBNKGS559k400nMwvVh3TmqH102ys3GJKUC2kV7qIIcdIya6AK1UBtR9IRe0BC9Ws/Wu/VhfY5b56zJzA76U9bXNyMjr70=</latexit> yt = f(ut, · · · , ut nu , yt 1, · · · , yt ny ) = f(xt) nu ny <latexit sha1_base64="70RphR5tJREZ+/PcGq/u0JOZRfc=">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</latexit> J = p 1 X t=0 (ˆ yt rt)2 + t(ut ut 1)2 + 0 @ µ ⇢ 2 ✓ + ut + µ ⇢ 2 + ✓ ut 4 ⇢ 1 A
b 50 <latexit sha1_base64="IE2DEecFHdKEhwOBWnoXWTqhB+Y=">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</latexit> ˆ y(x) = hw, (x)i + b = N X i=1 ↵iK(x, xi) + b <latexit sha1_base64="2U83NyY0vaT7mGTQk64XbYVFj2Y=">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</latexit> exp ✓ kx xik2 2 2 ◆ <latexit sha1_base64="tN3/rH7JZiA1yKEXBsScEZJpphE=">AAADDnicfVLNbhMxEPYufyVQSOHIZUREleZPu1FVuCBV4sIJBYm0lersyus4ianXu7W9TaLtvgNnrvAM3BBXXoFH4C3wJit+UtSxbH36ZvyNPTNRKrg2nvfDcW/cvHX7ztbd2r372w8e1nceHekkU5QNaSISdRIRzQSXbGi4EewkVYzEkWDH0dmr0n98wZTmiXxnlikbxWQq+YRTYiwV7jjbOOYyzOedqAN4wTt2B60CdgFPFKG5X+T9Al/O8WXQhzZQrLM4zPlLvwjeNG1syNurM2jtAcY1bNjC5DqL3jNqwCRglbqABZFTwWBuUwxmvLkI+B5Wa64LEbSXAQcbxc4BXxDFUs1FIm26lbSVhV0M1bpGqm2lutdKBS0r9kerpDq/PVN27oX1htfzVgZXgV+BBqpsENZ/4nFCs5hJQwXR+tT3UjPKiTKcClbUcKZZSugZmbJTCyWJmR7lq74V8MwyY5gkym5pYMX+fSMnsdbLOLKRMTEzvekryf/6SsYkidAbDzCTF6OcyzQzTNJ1/kkmyj6VswFjrmzbxNICQhW3XwA6I3YMjJ2gmq2Nv1mJq+Co3/MPegdv9xuH+1WVttAT9BQ1kY+eo0P0Gg3QEFHHOB+dT85n94P7xf3qfluHuk515zH6x9zvvwBiTu/1</latexit> min w,b,⇠,⇠⇤ 1 2 kwk2 + c N X i=1 (⇠i + ⇠⇤ i ) subject to hw, (xi)i b + yi " + ⇠i hw, (xi)i + b yi " + ⇠⇤ i ⇠i, ⇠⇤ i 0
p i. ii. b) s 52 <latexit sha1_base64="86rKDpv7EaLbrhvv3NPSOtzSZL0=">AAACL3icbZBNS8MwGMfT+Tbr29Sjl+AQPOhsZUwvwsCLeJrgXmAtI03TLSxtSpIKo/Rj+EE8e9XPIF7E676F6VZQp38I/Pg/z5Pk+Xsxo1JZ1rtRWlpeWV0rr5sbm1vbO5XdvY7kicCkjTnjouchSRiNSFtRxUgvFgSFHiNdb3yd17sPREjKo3s1iYkbomFEA4qR0tagchbDK3g6PIEOHGpy/EAgnDoxEooiBm+zb04y0zQHlapVs2aCf8EuoAoKtQaVqeNznIQkUpghKfu2FSs3ze/EjGSmk0gSIzxGQ9LXGKGQSDedLZbBI+34MOBCn0jBmftzIkWhlJPQ050hUiO5WMvNf2u5ozhncuEDKrh0UxrFiSIRnr8fJAwqDvPwoE8FwYpNNCAsqF4B4hHSiSkdcZ6NvZjEX+ic1+xGrXFXrzbrRUplcAAOwTGwwQVoghvQAm2AwSN4Bi/g1Xgy3owP43PeWjKKmX3wS8b0C3a/p4I=</latexit> p = g, g = @J @u <latexit sha1_base64="g1KEUdh5mAO6kMrLpKqXO4EKq3U=">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</latexit> p = H 1 g, G = @2 J @u2 <latexit sha1_base64="DIY5R1yfsAy1vLx6duOO5HUJVOA=">AAACI3icbVDLSgMxFM3UVx1fVZdugkVwUcuMlOpGKLhxWcE+oB1LJs20oZnJkNwRytAP8ENcu9VvcCduXPgB/oWZtgttPRA4nHMuN/f4seAaHOfTyq2srq1v5Dftre2d3b3C/kFTy0RR1qBSSNX2iWaCR6wBHARrx4qR0Bes5Y+uM7/1wJTmMrqDccy8kAwiHnBKwEi9QjHBV7iT9JwSxl3al6BLOOml8Zk78e67IGPbtk3KKTtT4GXizkkRzVHvFb67fUmTkEVABdG64zoxeClRwKlgE7ubaBYTOiID1jE0IiHTXjo9ZoJPjNLHgVTmRYCn6u+JlIRaj0PfJEMCQ73oZeK/XqaAlEIvfACCSy/lUZwAi+hsf5AIDBJnheE+V4yCGBtCqOLmBEyHRBEKptasG3exiWXSPC+71XL1tlKsVeYt5dEROkanyEUXqIZuUB01EEWP6Bm9oFfryXqz3q2PWTRnzWcO0R9YXz/bgqKG</latexit> u = [u0, · · · , up 1]> <latexit sha1_base64="3wvy4p/rWCAzKfzzcbwA58Y6W24=">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</latexit> min u0,··· ,up 1 p 1 X t=0 (ˆ yt rt)2 + t(ut ut 1)2 + 0 @ µ ⇢ 2 ✓ + nt + µ ⇢ 2 + ✓ nt 4 ⇢ 1 A